Green’s Dictionary of Slang

(US black) a police officer.

1957		H. Simmons Corner Boy 121: The bims is busting down the front door.
1962		(con. 1950s) H. Simmons Man Walking On Eggshells 213: Man, the bims around this mammy-tapping town is something, ain’t they?
1971		E.E. Landy Underground Dict. (1972).