a word of vague etymology, perhaps a convergence of two or more words, given wide application in late 19c. and settling into its main modern meaning "floozie" from early 1920s, with a revival in 1980s.
Bimbo first appears as the name of an alcoholic punch, mentioned in newspapers from New York state (1837), Boston (1842), and New Orleans (1844, but as having come from Boston). This sense quickly fades, though it occasional is on menus as late as 1895.
From 1860-1910, Bimbo as a proper name is frequent: It is the name or part of the name of several race horses, dogs, and monkeys, a circus elephant (perhaps echoing Jumbo), and a jester character in a play. It is in the title of a three-act musical farce ("Bimbo of Bombay"), and the name of a popular "knockabout clown"/actor in England and several other stage clowns. Also it appears as a genuine surname, and "The Bimbos" were a popular brother-sister comedy acrobatics team in vaudeville.
A separate bimbo seems to have entered American English c. 1900, via immigration, as an Italian word for a little child or a child's doll, evidently a contraction of bambino "baby."
By 1920 it began to be used generally of a stupid or ineffectual man, a usage Damon Runyon in 1919 traced to Philadelphia prize-fight slang. He wrote, that July, in a column printed in several newspapers, of a hotel lobby fist-fight between "Yankee Schwartz, the old Philadelphia boxer," and another man, which Schwartz wins.
"No Bimbo can lick me," he said, breathlessly, at the finish.
"What's a Bimbo?" somebody asked "Tiny" Maxwell, on the assumption that "Tiny" ought to be familiar with the Philadelphia lingo.
A bimbo," said "Tiny," "is t-t-two degrees lower than a coo-coo—cootie."
The word does turn up in Philadelphia papers' accounts of prizefights (e.g. "Fitzsimmons Is No Bimbo," Evening Public Ledger, May 25, 1920).
By 1920 the sense of "floozie" had developed (said to have been popularized by "Variety" staffer Jack Conway), perhaps boosted by "My Little Bimbo Down on Bamboo Isle," a popular 1920 song in which the singer (imploring the audience not to alert his wife) tells of "his shipwreck on a Fiji Isle and the little Bimbo he left down on that Bamboo isle." Its resurrection in this sense during 1980s U.S. political sex scandals led to derivatives including diminutive bimbette (1990) and male form himbo (1988).