Green’s Dictionary of Slang

fraudulent bail; thus broomstick, one who puts up such bail.

1699		N. Ward London Spy VIII 194: He has a rare knack at putting in Broomstick-Bail.
1812		Vaux Vocab. of the Flash Lang. in McLachlan (1964) 260: queer-bail Persons of no repute, hired to bail a prisoner in any bailable case; these men are to be had in London for a trifling sum, and are called Broomsticks.