Green’s Dictionary of Slang

(orig. US black) a girlfriend, a steady date.

1959		E. De Roo Go, Man, Go! 39: He just wants me around that’s all. Big Beano’s boss. He’s got to have a bam. He shows me off for a minute, then goes back to his motors.
1960		E. De Roo Big Rumble 34: I was Big Tony’s bam. Yeah, before he was busted by the fuzz I was his deb.
2000		(con. 1940s–60s) Décharné Straight from the Fridge Dad 7: Bam Girlfriend, steady date, parking date.