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.) an unattractive and/or ageing prostitute [the implication is of diseased matter].

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.