US 12 and US 20 are excellent roads for RVers.
Here's the official road opening dates for Yellowstone:
Yellowstone Road OpeningsHere's the campground opening dates to give you an idea of what's open in May.
As you can see, Fishing Bridge opens May 9 and it's an ideal spot for touring the park with full hookups. Advisable to make your reservations now but I don't know how crowded it would be in early May.
Yellowstone Campground Opening/Closing DatesYellowstone gets a LOT of snow and you'll probably see it in May. I would suggest a good time to go would be around May 15 to June 10. Then the summer crowds begin. Have a great trip!