Origin of "booty", meaning buttocks
Sex Slang (2007) by Tom Dalzell and Terry Victor says:
booty; bootie noun
1. the buttocks US, 1928
- He's Cyndi Lauper's boyfriend, so no skin search. Cyndi ouldn't want us looking up his boodie. - James Elroy, Suicide Hill 1986
2. the vagina US, 1925
- I've got a body as well as a booty. - Partlet, Booty Snatchers 1979
(The Concise New Partridge Dictionary of Slang and Unconventional English (2007) by Eric Partridge, Tom Dalzell and Terry Victor gives a subset of this same definition.)
The OED expands on these same two definitions, but with a wider gap in earliest use:
1. Sexual intercourse; a person (esp. a woman) regarded as an object of sexual ambition or desire. Also (occas.): the female genitals. Cf. ass n.2 1b [sexual gratification. Also, a woman or women, regarded as an object affording this.].
1926 C. Van Vechten Nigger Heaven ii. iii. 215 Now..that you've gone white, do you really want..pinks for boody?
And:
2. The buttocks.
Prob. the earlier sense, esp. given the similar sense development of ass n.2, pussy n. 3, etc.1959 F. L. Brown Trumbull Park 363 Getting kicked in the booty would be mighty discouraging too.
Their etymology is:
Probably an altered form of botty n.; compare batty n.2 Perhaps influenced (especially in sense 1) by booty n.1 [Plunder, gain, etc.]
The OED suggests that, in this sense, booty might be a variant of botty, which in turn is a reduced form of bottom. If so, the fact that it has the same spelling as the word meaning ‘plunder’ is a coincidence.
The term booty (buttocks, bottom, whatever) used (usually in the collective sense) to refer to a woman or women in general as sexual objects is a form of synecdoche:
A figure of speech in which a part is used for the whole (as hand for sailor), the whole for a part (as the law for police officer), the specific for the general (as cutthroat for assassin), the general for the specific (as thief for pickpocket), or the material for the thing made from it (as steel for sword).
It's the equivalent of referring to ass or pussy as a stand-in for woman-as-sexual-object. You hear this usage all the time.
The British refer to a car's trunk as the boot. The OED entry for boot is "3 British An enclosed space at the back of a car for carrying luggage or other goods."
In the car designs of the early 1900s onward, the attractive boots of cars did remind one of bums, human or other animal such as horses.
A related term is "dicky" which the OED states is "2 dated, chiefly British A folding outside seat at the back of a vehicle."
It didn't take a very old schoolboy to put 2 and 2 together. They wouldn't learn the term misogyny for several more years.