We live close and were in Coulter Bay last September. They were upset because the water level was very low. If you are in Yellowstone, when done head for Jackson from the park though the (I think its the south entrance) not sure I just drive. Coulter Bay is on the way to Jackson. You will cross the Continental Divide three times 6 to 8 thousand feet two lane roads in very good shape with lots of pull outs. Our Class C had no trouble with the V-10.
There are two places to camp. The camp ground allows no RV longer then 25 feet. If longer you must go to the other camp ground, a mater of turning right or left. It has hookups and a hefty 50 plus dollars a night.