bust n.1

Middle English bresten, from Old English berstan (intransitive) "break suddenly, shatter as a result of pressure from within" (class III strong verb; past tense bærst, past participle borsten), from a West Germanic metathesis of Proto-Germanic *brest- (source also of Old Saxon brestan, Old Frisian bersta, Middle Dutch berstan, Low German barsten, Dutch barsten, Old High German brestan, German bersten "to burst").

The forms reverted to brest- in Middle English from influence of Old Norse brestan/brast/brosten, from the same Germanic root, but it was re-metathesized late 16c. and emerged in the modern form, though brast was common as past tense through 17c. and survives in dialect.

In Old English "Chiefly said of things possessing considerable capacity for resistance and breaking with loud noise; often of cords, etc., snapping under tension; also of spears, swords, etc., shivered in battle" [OED]; in late Old English also "break violently open as an effect of internal forces." Figuratively, in reference to being over-full of excitement, anticipation, emotion, etc., from c. 1200.

The transitive sense ("to cause to break, cause to explode") is from late 13c. The meaning "to issue suddenly and abundantly" is from c. 1300 (literal), mid-13c. (figurative). The meaning "break (into) sudden activity or expression" is from late 14c. Related: Bursting.

"backside," attested by 1860 in nautical slang, in popular use from 1930; chiefly U.S.; from dialectal variant pronunciation of arse (q.v.). The loss of -r- before -s- is not uncommon (burst/bust, curse/cuss, horse/hoss, barse/bass, garsh/gash, parcel/passel).

Indirect evidence of the change from arse to ass can be traced to 17c. By 1680s arse was being pronounced to rhyme with "-ass" words, as in "Sodom or the Quintessence of Debauchery": "I would advise you, sir, to make a pass/Once more at Pockenello's loyal arse." It is perhaps as early as Shakespeare's day, if Nick Bottom transformed into a donkey in "A Midsummer Night's Dream" (1594) is the word-play some think it is.

I must to the barber's, mounsieur; for me thinks I am marvellous hairy about the face; and I am such a tender ass, if my hair do but tickle me, I must scratch. [Bottom]

By 1785 polite speakers were avoiding ass in the "donkey" sense. 

The meaning "woman regarded as a sexual object" is by early 1940s (piece of ass seems to be implied in 1930s Tijuana Bibles), but the image is older (compare buttock "a common strumpet," 1670s). To have (one's) head up (one's) ass "not know what one is doing" is attested by 1969. Colloquial (one's) ass "one's self, one's person" attested by 1958. To work (one's) ass off "work very much" is by 1946; to laugh (one's) ass off "laugh very much" is by 1972 (implied from 1965). The (stick it) up your ass oath is attested by 1953; apparent euphemisms suggest earlier use:

He snoighed up his nose as if th' cheese stunk, eyed me wi an air o contempt fro my shoon to my yed, un deawn ogen fro my yed to my shoon ; un then pushin th' brade un cheese into my hont ogen, he says "Take your vile bread and cheese and stick it up your coat sleeve, and be demmed to you. Do you think I want your paltry grub?" Un then, turnin on his heel, he hurried into th' perk. ["Bobby Shuttle un His Woife Sayroh's Visit to Manchester," 1857]