shayna1030,
Not a dumb question at all -- I too have a need to "recycle" water often.

And you are certainly captive in the bus! You might want to call the tour organization and ask them about this. I would imagine that the seats in the main cabin would be relatively roomy, but I also would imagine that the bus manufacturers are not going to use up precious space on the "little private room". Bus tours generally make sure that they stop every couple of hours at a highway rest stop, so that folks can stretch their legs, make a dash for the rest rooms, grab a cup of coffee (which of course makes the dash to the rest room necessary at the next pause!).
Do enjoy your visit to New York!
--Rheanna