Thanks, I will pass that along to him!

We sang
If you miss me at the back of the bus,
You can't find me nowhere,
Come on up to the front of the bus,
I'll be riding up there.
I'll be riding up there,
I'll be riding up there, oh-oh,
Come on up to the front of the bus,
I'll be riding up there.
And a lot of other verses, very close to both those you posted above. One summer about a dozen of us built some bath houses, concrete block with showers, toilets, sinks for a community that had none. That was basically our theme song, and was far my favorite of all of that ilk. Some verses were made up on the spot, not surprisingly, but some were very like the Carawan verses. I like the 'swim' verse because of the rhythm of fitting in 'Mississippi River.'

We differentiated between 'road' songs and 'basement' songs which seem to be both included in these 'back of the bus' songs in this thread. A 'road' song is solely to pass the time (99 bottles or the ants for the little kids, more elaborate ones for the older kids, maybe cumulative, or lots of verses, or harmony or rounds). A 'basement' song is one we 'young ladies' did not sing in public, usually bawdy, sometimes pretty vulgar.
I learned 'Back of the Bus' on the same night and from the same teen from whom I learned 'Hot Nuts' of the basement genre. ('Nuts, hot nuts, you get them from the peanut man; nuts, hot nuts, you get them any way you can' seemed terribly racy then though I am not sure why; I suspect the verses were noticeably ruder but I do not happen to recall any of them.)