Green’s Dictionary of Slang

(US black) to laugh.

1897		‘Mark Twain’ Tom Sawyer, Detective 77: Then he busted out, and had another of them forty-rod laughs of his’n.
1945		W.R. Burnett Tomorrow’s Another Day 91: ‘The boss practically had him rolling on the floor, laughing. I almost busted out myself a couple of times’.
1992		R.C. Cruz Straight Outta Compton 13: Bosco busted out, wiping his forehead. ‘It ain’t funny,’ Flip said.