Maybe my memory is faulty, but I don't recall a lot of rushing traffic on Beartooth. Everyone was more interested in absorbing the sights than in getting to Yellowstone fast. But then I drove it in mid September with threat of snow flurries. You certainly need to know how to safely climb and descend 5000', but the grades and curves not exceptional. If you can drive a freeway cloverleaf exchange you can handle the curves on Beartooth.
Someone brought up Glacier's Going to the Sun. The big difference is that GtS has long stretches with a rock cut on one side, and low retaining wall on the other. The long rear overhang of an RV could easily project into the oncoming traffic lane. The park has strict length and width restrictions (and height due to rock overhangs). There is nothing like that on Beartooth.