Did the slang term "The Bomb" meaning "Very Cool" come from the American Jazz scene?
Solution 1:
Summary
I can't find any evidence to suggest this is a jazz term, and the earliest example I found is from 1995. The alternative da bomb dates from at least 1994.
There's no entry in a number of slang dictionaries (A Jazz Lexicon, A Dictionary of Slang and Unconventional English, Shorter Slang Dictionary, The Slang and Jargon of Drugs and Drink, A Dictionary of Cliches, American Heritage Dictionary of Idioms, British English A to Zed). This suggests it's a recent term.
'50s claims
Like your linked Jazz Slang, it's often claimed to be 1950s or jazz slang but there's no evidence for it. This list of 50's Slang includes:
The Bomb --- Very cool.
The Crusader's new disc, "Louisiana Hot Sauce" is "the bomb."
The list is undated but was first archived in 2002. Further, The Crusaders' released Louisiana Hot Sauce in 1996. The others all seem to be copies of this (or another).
OED
Although not exactly the same, the closest thing in the OED is:
1e. A success (esp. in entertainment); also U.S., a failure. So phr. like a bomb and varr., with great speed; with considerable effectiveness or success. colloq.
Here's the first and a couple of other quotations:
1954 Amer. Speech 29 99 Like a bomb,..very fast.
1961 New Yorker 28 Oct. 43/2 What had once been called a failure became a ‘bomb’.
1963 The Beatles 5 Once, Paul McCartney and I played Reading as the Nurk Twins. Went down a bomb, I recall.
All the quotations are "a bomb" not "the bomb" and are quite different.
Lexical Investigations
The only relevant quotation from your linked Lexical Investigations: Bomb is fairly recent:
“Your magazine is the bomb! I really like the comics and when you make fun of that Spears girl.”
—Spin, September 2002
Google Groups
The earliest "is the bomb" I found in Google Groups (there may be earlier, but Google recently redesigned Groups and crippled the search) is this exchange from August 1996:
On 21 Aug 1996, Cheezmelt wrote:
If I wrote a song, it'd be called " Beck is the Bomb"
And it would be the Bomb.
Or maybe it would be called "Loopity loo and your mom too"
I haven't decided
Geez don't you kids know anything?
whenever something is the bomb,
and you specify that it is THE bomb,
you must follow it with the phrase, YO.
for example, "that shit was the bomb, yo!"
as opposed to:
when something is merely bomb, and there
is no the, then you would say something like
"That's some bomb acid!"
stay in school!
There's nothing before 1996, and quite a few after and into the 2000s and this decade.
Subzin movie subtitles
The earliest I found in film subtitles is the 1995 Spike Lee film Clockers which uses it twice:
00:04:35 # Blue collar comes to bourgeois
00:04:37 # Depressed in your chest... #
00:04:39 - Chuck D is the bomb, boy. - What?
00:04:41 Get the fuck outta here. Chuck D ain't shit.
00:04:44 That nigger Chuck D is assed out, and the rest of Public Enemy.
And:
01:12:18 - One drink? Wasn't drunk? - Nope.
01:12:21 - He was rude. - (Bartender) Yeah.
01:12:26 'Ooh! I'm just gettin' warmed up. But it's The Bomb.'
01:12:30 Was he with anybody?
01:12:33 He came in alone. Might've had a conversation.
The film was released in September 1995 and based on a 1992 book by Richard Price, although the book doesn't appear to use the phrase.
"Da bomb"
There's even more and earlier Google Groups results for the variant da bomb, such as this from soc.culture.filipino in December 1994 ("SCF at REDj is DA BOMB...."):
Actually, "DA BOMB" is part of the continuous urban parlance that Filipino teenagers tend to borrow from African American teenagers. "DA BOMB" is a comprable adjective to such words used in the past, like "swell," "groovy," "cool," "radical," "gnarly," "awesome," "def," and "hype."
Elson
Urban LingustDr. Vicente Rafael, a Filipino-American and an associate professor at UCSD's communications department describes this phenomenon as "downward assimilation"; Filipino-American teenagers borrow the language, clothes, and mannerisms from pop black culture because they perceive it to be a more sexual, more agressive (as in violent) culture, characteristics which they perceive to be wanting in their own native culture.
A few days later in the same group ("*** DA BOMB ***"):
OKay ppl... I haven't been posting as on SCF due to the fact I'm forming a new IRC channel w/ MinMei aka NeuSpeed. This new channel will hopefully be Da BOMB.... N E Wayz... I see that ppl responded to the comment I made at REDj's party...
The Party Was Da BOMB (the best in the West)... and it seems that ppl around here (Elson, Rhett...) no names will be mention seems to put that title to me... Okay Elson... I'll go on an airplane and say to the pilot this "Da BOMB"!!!! =) NE Wayz.... look out for the new channel...
There's an earlier use in comp.sys.mac.apps from July 1994. The post discusses Apple computer crashes ("Has anyone else had problems with Appleshare causing a system bomb on startup?") but the subject seems to be a passing reference to the phrase:
Appleshare and "da BOMB"
Solution 2:
Early dictionary/glossary coverage of 'bomb' and 'the bomb'
Geneva Smitherman, Black Talk: Words and Phrases from the Hood to the Amen Corner (1994) has this entry for "the bomb":
THE BOMB 1) The height of something; the ultimate quality of anything. 2) An outstanding grade of marijuana.
J.E. Lighter, The Random House Historical Dictionary of American Slang (1994) traces early instances of bomb in both of the senses that Smitherman reports:
bomb n. 1.a. any unexpected statement or developmant having a sudden sensational effect. Now colloq. [First citation is to a Chicago Tribune headline from 1918.] ... b. something excellent or unusually successful; DYNAMITE; a SMASH. 1974 V. Smith Jones Men 23: Nice....Thi is a bomb, baby. 1974 Odd Couple (ABC-TV): With the right person playing Scrooge it could be a bomb. 1989 S. Robinson & D. Ritz Smokey 218: I had all the tunes done, except I knew the real bomb was still on Marv's demo tape. ... 3. Narc. a. a large or potent marijuana cigarette. 1951 Kerouac Cody 24: In fall 1950 when I was so much on weed, three bombs a day. 1964 Larner & Tefferteller, Add. in Street 33: I paid 75 cents a stick, or dollar for a bomb. ... 1967 Rosevear Pot 157: Bomb: A fat, or thick, marijuana cigarette. Also...[one] with fast-acting qualities.
Lighter identifies one sense of bomb as having arisen expressly in the context of jazz:
[6.]b. Jazz. a heavy drumstroke. 1953–58 J.C. Holmes Horn 39: Lecturing another [drummer] on "Them bombs you always dropping on the bridge." 1961 R. Russell Sound 73: "How about this kid Tiny he had on drums?"..."He dropped too many bombs. Red was dragged real bad after the first week."
Clarence Major, Dictionary of Afro-American Slang (1970) provides an interesting view of the "bomb" landscape in African American slang circa 1970:
Bombed out: overcome or dominated by an excess of narcotics.
Bomber: a very thick reefer (marijuana).
Bombs: (1940's) word used to explain the effect of Kenny Clarke's drum accent after bebop become simply bop.
These definitions tend to support Lighter's entries above, though the dates for the drumming sense of bombs differ somewhat.
Early use of 'the bomb'/'da bomb' in relevant senses in song/rap lyrics
One early relevant use of "the bomb" in music lyrics appears in DJ Quik, "Tonite," from his Quik Is the Name CD (1991):
Ham is in the bedroom rollin' up a stencil/Fatter than a pinky and the length of a pencil/Freakie lit it up and hit it one two three/Shabby took a hit and then they pass it to me/It's the bomb!/Yo, I can feel my senses get numb!
This is obviously "It's the bomb" in the marijuana sense of the word, but it can also be understood as hinting at "It's sublime."
Kris Kross released an album titled Da Bomb in 1993. The title track ("Da Bomb") includes these lyrics:
It's da bomb, it's da bomb/I drop bombs like Hiroshima/It's da bomb/I know you hear me comin, here I come/So you besta watch ya back/It's da bomb/I know you hear me comin, here I come/And I'm called the Miggida-Miggida-Mac
Here "da bomb" means something like "the powerful, explosive thing"—which might be actual weaponry, or rap lyrics, or some other unspecified thing.
Conclusion
Though I don't have absolute confidence in the dates of the cited song lyrics from DJ Quik's "Tonite," I think it is probable that "the bomb" was in use as African American slang at around that time (1991) in the two senses that Smitherman cites three years later in Black Talk.