Green’s Dictionary of Slang

bust out v.1

[bust v.1 (2b)]

(orig. US) to betray secrets.

[US](con. c.1840) ‘Mark Twain’ Huckleberry Finn 234: I reckon I couldn’t a stood it all, but would a had to bust out and tell on our gang.
[WI]Francis-Jackson Official Dancehall Dict. 7: [...] 2. to reveal, let the cat out of the bag.