Green’s Dictionary of Slang

an illegal establishment, e.g. a casino, a burlesque theatre.

1938		D. Runyon ‘The Big Umbrella’ in Runyon on Broadway (1954) 550: A bust-out joint being a joint where they will cheat your eyeballs out at cards, and dice, and similar devices.
1952		Lait & Mortimer USA Confidential 251: The Hide-Ho, in Newport, is a bust-out joint, with whores and gambling.
1956		‘Toney Betts’ Across the Board 246: The race-track managements encouraged touting, regarding the parasites as steerers for their bust-out joints.
1959		‘Monroe Fry’ Sex, Vice & Business 8: Bust-out joints, of which there are some two dozen in Newport, got their name from the recognized practice of not letting a customer out until he's ‘bust,’ one way or the other.
1975		J. Roe Same Old Grind 83: [of a burlesque theatre] ‘Don’t worry, Mahmoud [the theatre’s owner] don’t ask you to mix heavy, this is no bust-out joint’.
1977		P. Hamill Flesh and Blood (1978) 235: She’s singing here downtown. Down in one of the bust-out joints.