Flying Bridge inside Yellowstone only has a few sites that will accomadate the larger rigs so you would need to call and make a reservation (as soon as possible!). The drive in from the East entrance is a piece of cake. I was in a 40' bus conversion towing a full size extended Chevy van. The roads are excellent and wide. Take all the time you need if you have any concerns.
The Grizzly recommendation is an excellent one as well as the Mammoth campground if you want to stay outside the park. It just adds to the drive time involved but it just means you have to break your visit up into sections and only visit one (maybe 2) or the major attractions on each visit.
Have a great trip. Go early in the year (May/June) or late (Sept/Oct) for the best experience, the most animals and the least number or humans!