My best guess is that someone tried to get cute and used "bumming" to replace "mooning".
Since I'm not completely sure if this was a purely American practice, or if it continued after... oh, the '70s, I should probably explain. "Mooning" was the practice of turning around and dropping trousers and showing your naked ass to someone.
I know. I never quite understood it either.
Any road, my best guess is that one of my fellow Americans knew enough British colloquialism to know the word "bum" is used when we might use "butt" or "ass". But, didn't have the first clue beyond that and chose to try using it to replace "mooning".