First RV (old class A), and want to take it to Yellowstone

reservations are definitely needed at Fishing Bridge campground in Yellowstone. You didn't say when you were going. Coach Net Road service would be well worth the price. If they are booked up, ask this forum for other options. They do have other campgrounds with no hookups. Ask yourself what's the worst thing that could happen and have a plan for that and go for it!