Jim went over to hit on that girl at the bar, but as he opened his mouth, he felt he was about to bust a move, so he continued toward the patio outside.
The original usage of this phrase is "to dance." It was popularized in the 1989 single of the same name by rapper Young MC, who tells (in the song) of his several attempts to find (or seduce) a woman in various places and failing to be able to do so because he can't dance; he isn't able to "bust a move."