Green’s Dictionary of Slang

1. (Aus.) a football.

1906

Punch (Melbourne) 27 Sept. 4/1: Yercudn’t ’old ther greasy ball, and yercudn’t bounce ther bladder, and yercudn’t run, and yercudn’t do nuthink.

2. (US Und.) a prostitute, usu. ageing/unattractive [the implication is of diseased matter].

1926		‘Let me sit and rest, stranger’ in Canfield Coll. I got stuck on a bladder called Fanny, / And she wher [sic] clean out of sight / She could fuck like a mink in the daytime / And suck to a finish at night.
1935		W. Smith Bessie Cotter 252: I’ve seen some old bladders throw a fit and claim where they just can’t stand men any more.
1939		D. Maurer ‘Prostitutes and Criminal Argots’ in Lang. Und. (1981) 117/1: bladder. An unattractive prostitute.