A scenic 45 minute drive from Bozeman took us to Norris Hot Springs -- a natural spring -- no chlorine -- private -- with organic food for sale -- The pool has constantly running mineral water -- There is a parking lot where trailers and RVs can get hookups (I think full, but not sure) but it is definitely nothing more than a parking lot.
One more thing about campgrounds in Bozeman -- if you're passing through and don't need to be close to downtown -- the KOA that we passed up is directly next to a place called Bozeman Hot Springs -- it has several different pools with varying temps -- we passed it up in favor of Norris because most of the pools are inside and it was too beautiful to be inside -- but it is open all year round.