Combination of two phrases, the first being "Bumbling Idiot" and the second being "Fuck Up." Making the combined definition of the two: an individual who lacks coordination and social graces thus imparing them in such a way that their actions cause catastrophe.
Officer Number One: Did you see Johnson shoot that gun in fully automatic on the range and trip and take out a whole convoy on accident, I mean JESUS!
Officer Number Two: Yeah, what a damn Bumble Fuck.