Green’s Dictionary of Slang

brum n.2

[? brum adj.; she is an ‘inferior’ form of woman or var. of brim n.1 (1)]

(US) a prostitute.

[US]T.A. Dorgan in Zwilling TAD Lex. (1993) 21: Every bloke had to bring his ‘bundle’ wid him, an’ if he couldn’t find one Chuck had a couple o’ ‘brums’ on de side that was widout a partner.
[US]Monteleone Criminal Sl. (rev. edn).
[US](con. 1950-1960) R.A. Freeman Dict. Inmate Sl. (Walla Walla, WA) 18: Brum – a prostitute, harlot, etc.