A bath takes nearly 30 gallons of water so you are goiing to need park water and sewer, no holding tank for that amount.. Now just so you know today they have bath tubs where you open a door, walk in and sit down... Some of those are within 1" of the size of a standard RV shower. (Or even less)
I'd use a Demand type water heater with it if I were installing.. And some day.. I just might do that.