I remember seeing it as a kid, but never saw it when my kids were watching in the early aughts. It started out with a hippie looking puppet going "bum bum; bum bum bum bum bum; bum bum bum BUM, bum bum bum bum. Others came and joined in; I remember Grover, and maybe Prairie Dawn. It isn’t Mahna Mahna.
I think you got it! I knew the OP’s description of the song sounded familiar, but I had nothing.
That’s it! I didn’t find it because I searched “bum, bum” instead of “bom, bom,” Of course it well over 50 years ago that I last saw it. When I was in Boy Scouts we’d sometimes sing it on hikes.