There are two songs I tend to sing to myself if I really have to shit but can't at that precise moment (in transit, someone's already in the b-room, etc).
The first is a variation on the famous first line of the "It Takes Two". In my version, it's "I wanna dump right now", or often with a bunch of repeats/stutters like "I wanna/I wanna/I wanna/I wanna/I wanna/I wanna dump right now".
The second comes from a commercial from the 90s that I can't seem to remember what it was for. It was a cartoon character talking about either a board game or something edible, who at the end of the ad went "excuse me... while I chomp". Like for Hungry Hungry Hippos but not. I don't remember. Anyway, my variation is "excuse me... while I dump".