Etymonline tends to back up MrHen's guess:
variant of burst, 1764, Amer.Eng. The verb sense of [...] "arrest" is from 1953 (earlier "to raid" from Prohibition).
Unfortunately this doesn't give us a lot of insight into how that meaning involved, but "bu[r]sting in" to places where criminal activity is going on is as good a guess as any.