Hopefully Jamawani will chime in.
I rode in the area a few years ago with a guy who has ridden the Beartooth Highway about 10 times, he said it is incredible, but you have to be prepared for weather any time of the year. Sunlight Basin/Chief Joseph Highway to Cody is also spectacular, and a bit lower so if there is weather that would be a good option (I rode that one, and I would recommend it over heading through Yellowstone, it is empty of cars and stacked with scenery).
Having said I haven't ridden the Beartooth, here's what I would do:http://g.co/maps/mx8qh
I have ridden this route from Tensleep (I came out of Yellowstone at Cody) to the black hills, and it is great. I rode over the Bighorns eastbound from Tensleep to Buffalo (awesome) and also westbound from Sheridan to Shell / Greybull (also awesome, slightly less spectacular). I hear (but have not done) that the road up into the bighorns from Lovell is incredibly steep, so you might consider if you want to go that way or not, depending on how much you like steep. Other hightlights of the route are Devil's Tower, quiet roads to Belle Fourche, and SPearfish Canyon. THe stretch between Buffalo and Gillette is pretty empty, there are just enough services but be sure to take plenty of water.
In any case, do go through the bighorn mountains, they are the best.