How did 'drone' come to mean both 'one who does no work' and 'one who spends most of his or her time doing menial work'?
As early as 1575, drone was defined as a lazy idle sluggard. From page 313, the Note-Book and Word-List of Appius and Virginia in John Stephen Farmer's Five Anonymous Plays:
Dronel (A.V. 4id), a generic reproach : a derivative of drone = lazy idler, sluggard. Murray only gives two instances of its use : one the passage now in question ; the other from Stubbes' Anatomy of Abuse — "Like unto dronels devouring the sweet honey of the poor labouring bees."
Phillip Stubbes, et al, went on at length about lazy idlers, using the image of drone bees in A Phillip Stubbes's Anatomy of the Abuses in England in Shakspere's Youth:
One sort is of stout, strong, lustie, couragious, and valiant beggers, which are able to worke, and will not. These at no hand are not to be relieued [extensive argument omitted]... These are as drone bees, that liue vpon the spoile of the poore bees that labour and toile to get their liuing with the sweat of their faces. If such fellowes as these will not worke, but liue upon begging, let them be punnished and imprisoned till they be content to worke.
The few male bees that inhabit the hive of honey bees have no other function than to fertilize the queen bee:
Unlike the female worker bee, drones do not have stingers and do not participate in nectar and pollen gathering. A drones' primary role is to mate with a fertile queen.
Drone bees also produce a distinctive sound:
After take-off drones produce characteristic sound which is different from sound produced by flying workers.
This sound distinctive sound influences two of the verbal definition, and several of the noun definitions of drone, and some intuitively suggest the possibility that the lazy connotation, combined with the sound effect, leads to the fourth noun definition of the OP. It is true that drone was applied routinely to industrial machinery from the early 20th century, as on pGE 184 of The Inheritors: An Extravagant Story, but there is no evidence of this development.
There seems to be two parallel tracks in the development of the meaning one who is obliged to do menial work. First, in 1913, the International Molders' and Foundry Workers' Journal published and ode to Labor Day:
You bend the strike-breaker unto repentance.
The drone worker gluttons at thy shrine.
You electrify the ambition of every union man for the coming of another Labor Day in his inevitable March of Progress.
[Omitted lines]
Know you, you drone worker, that he, even if he be toiler, who profits industrial gain by the sweat of another without himself giving full aid is like the unscrupulous money lender, an usurer.
Publication emphasis
By applying the notion of lazy idler and sluggard to people who were working--but not profiting the union movement with full aid--this usage opened the door to drone meaning the menial worker--especially the one who displays loyalty to the corporate boss.
The meaning of this expression is reinforced in 1917 by Volume 19 of Journal of the Switchmen's Union, which contained an article on pages 161-2 referring to these drones:
Victories of Labor Achieved by Workers--Not by Drones
Regardless of the drones in the labor movement, the active workers keep busy its varied workings...Every human agency for the promotion of a better, brighter or more useful condition in life finds itself encumbered to some extent by a load of drones seeking to better survive at its expense, without contributing anything towards its encouragement or support. [extended discussion omitted]... Labor union beehives have their full complement of them and they appear to perform about the same functions as the drone bee does in the beehive: propagation of the species and living on the nectar the workers have gathered in for sustenance.
In a letter from the Assistant Vice President on pages 610-11, the same publication published:
As the tree is strengthened by the cutting away of dead limbs, which are the reactionary elements, so the Switchmen's Union may be imporved by weeding out the drones, the slackers, the knockers and those who think more of the friendship of the men who are helping to crucify them than they do of their own union.
Out of this milieu, the word drone found a place in a famous union anthem, Solidarity Forever:
All the world that's owned by idle drones is ours and ours alone.
We have laid the wide foundations; built it skyward stone by stone.
It is ours, not to slave in, but to master and to own.
While the union makes us strong.
The evidence suggests that the meaning one who is obliged to do menial work may also be connected with definition three:
an unmanned aircraft or ship guided by remote control
Emphasis mine
This use of drone for unmanned aircraft goes back at least to a 1939 reference on page 101 of G. & C. Merriam Company's Word Study - Volumes 15-29:
Thus a distinction is made between a drone plane and a guided missile:
Drone – a remotely controlled aircraft.
Guided missile – an unmanned vehicle moving about the earth's surface, whose trajectory or flight [is prearranged]Emphasis mine
It is not clear which influenced the choice of drone unmanned aircraft more, but the meanings eventually merged into one:
- The droning sound of the airplane engine
- The perception of drone workers as automatons of corporate bosses
The sense of remotely controlled person was clearly expressed in 1942 on page 67 of Logan Wilson's The Academic Man: A Study in the Sociology of a Profession:
From the university angle, non-cooperation is a form of incompetence, and by ingenious definition the 'safe' yet mediocre drone may be deemed competent, and the intellectually alert, conscientious, but socially unorthodox person may be branded as incompetent.
Life Magazine reinforced the sense of mindless automaton with the expression neuter drone on page 34 of its Jun 3, 1957 article entitled America the Beautiful?:
The closer we huddle together, the greater this pressure for conformity becomes ... breeding swarms of neuter drones [discussion omitted]... Up to now we have heard nothing but charges of conformity. Some of our recent books have been scaring the pizzazz out of us with the notion of a Lonely Crowd in which "other-directed, radar-attuned" Americans wander voiceless and intimidated, bossed by a Power Elite (themselves afflicted with an Executive Neurosis and harried by conformist Executive Wives), flim-flammed by Hidden Persuaders and emasculated into a neuter drone called the Organization Man.
It seems quite clear that when drone is used as one who is obliged to do menial work, the connotation is that his boss is doing all the thinking for him. This meaning can be traced back to the development of automated aviation technology, and probably farther back to the union movement of the early 20th century.
By way of adding a supplement to ScotM's very good answer, I will focus on the question "when did the connection [of drones] to menial (especially) or routine and boring work arise?"
To gauge actual usage, I will rely on the definitions provided by dictionaries through the years. This is an inexact measure, obviously, because dictionaries typically are in no hurry to embrace new meanings of established words. But on the other hand, when a definition does appear in a dictionary, it indicates that a fairly strong degree of acceptance and use in the language, which seems worth identifying in its own right.
Dictionary definitions of 'drone' from 1616 through 1895
The earliest dictionary definition of drone that I have been able to find is from John Bulloker, An English Expositor: Teaching the Interpretation of the Hardest Words Used in Our Language (1616):
Drone. An idle Bee that will not labour.
From John Kersey, Dictionarium Anglo-Britannicum: or, a general English Dictionary (1708):
Drone, a kind of Fly or Wasp without a sting ; also a slothful Fellow.
From Thomas Dyche & William Pardon, A New General English Dictionary (1735):
DRONE (S.) A Bee without a Sting, which the rest drive out of the Hive ; also an idle, slothful, indolent Person.
From Samuel Johnson, A Dictionary of the English Language (1756) and its definitions of the noun and verb forms of drone:
DRONE. s. 1. The bee which makes no honey. Dryden. 2. A sluggard ; an idler. Addison. 3. The hum, or instrument of humming.
To DRONE. v.n. To live in idleness. Dryden.
So already in 1756 we have drone in the sense of the idle bee, the idle human being, and the hum. As is often the case, Noah Webster, A Compendious Dictionary of the English Language (1806) seems more than a little indebted to Johnson for the wording of its definitions:
Drone, n. the male bee, sluggard, idler, hum in music
Drone, v.i. to live in idleness, to dream on
Webster's American Dictionary of the English Language (1828) adds a fourth definition for the noun drone ("the largest tube of the bag-pipe, which emits a continued deep note"), and a second definition for the verb drone ("To give a low, heavy, dull sound ; as the cymbal's droning sound. Dryden").
In Webster's Academic Dictionary (1867), the only significant change is that the bagpipe drone is now listed separately under drone pipe. The Academic Dictionary of 1895 adds no new definitions.
Dictionary definitions of drone from 1916 to the present
Webster's Third Collegiate Dictionary (1916) adds one new definition of the noun *drone to the ones noted in the 1895 Academic Dictionary:
One who speaks monotonously, as with a drawl.
The next major addition is reported in Webster's Sixth Collegiate Dictionary (1949), again involving a new meaning of the noun drone:
A pilotless airplane, vessel, or other craft remote-controlled by radio, as for target purposes or ammunition-laden for blasting enemy defenses.
This new definition is something of a curiosity. On the one hand, the name drone seems quite fitting for an unarmed airplane or boat used for target practice (especially since the same dictionary notes of the "male bee" drone, "It has no sting and gathers no honey"). But the only things that the target practice drone has in common with the ammunition-laden assault drone are radio control and a short life span.
The Seventh Collegiate (1963) drops the discussion of the uses of drone aircraft and seacraft, producing a much shorter version of that definition:
a pilotless ship or airplane controlled by radio signals
The Seventh Collegiate also marks a change in the longstanding wording of "live in idleness" definition of the intransitive verb drone:
to pass, proceed, or act in a dull, drowsy or indifferent manner
and introduces a new definition of the transitive verb drone:
to pass or spend dully
The implications of these verb definitions become clearer in the Eighth Collegiate (1973):
[vi:] to pass, proceed, or act in a dull, drowsy, or indifferent manner
[vt:] to pass or spend in dull or monotonous activity or in idleness {droned away the precious years of youth}
At this point, the long-recognized torpor of inactivity is explicitly joined by the torpor of monotonous activity. All that remains is to discover the noun drone in the sense of one who engages in monotonous activity—which Webster's Ninth Collegiate (1983) does very economically, adding the one-word definition "DRUDGE." The Eleventh Collegiate (2003) notes that the relevant senses of drudge are "one who is obliged to do menial work" (a definition that goes back to Johnson's 1756 dictionary) and "one whose work is routine and boring."
Conclusions
To sum up, Merriam-Webster's Collegiate Dictionary series has explicitly recognized the noun drone in the sense of "drudge" only since 1983, though it found a drudgery-friendly sense of the transitive verb drone ten years earlier, and showed signs of recognizing that sense of the verb another ten years before that.
The crucial aspect of Merriam-Webster's transitional definitions of the period 1963–1983, I think, is the element of dullness: Whether a person is passing the time, proceeding toward a destination, acting on something, or laboring away at a monotonous task, if the thing being done is dull enough, the person engaged in it is droning (and by 1983, is a drone).
Given this chronology, it seems that drone came to mean both "deadbeat idler" and "menial laborer" by reference to the male bee—not because the male bee is sometimes idle and sometimes engaged in menial labor—but because the male bee is dull, and both idleness and drudgery are dull, too. Ultimately, in English, the work habits of the male bee, or of the human drone, simply aren't as important as the creature's celebrated listlessness.