Not Yellowstone but nearby, the Beartooth highway (Red Lodge) and Gravelly Range road (Ennis), both spectacular scenery, Very weather dependent.
I will second the Beartooth. My all time favorite highway. In the same area is Dead Indian Pass/Chief Joseph Highway. They are just outside of the park but much more suited for a Wanderer plus the camping would better....no NPS little camp cities.
Slough Creek campground, which is in the park, is my favorite NPS camp because it is in prime wolf habitat, is the least improved and is close to Cooke City, MT and the Beartooth.
I'll probably be up there around the same time frame. Look for this:
Griz will be looking to put on weight for the winter. Rumor has it they like older/slow gentlemen with funny hats.
Some pictures of the Beartooth area.
Note the tooth
Have you been to Glacier NP yet?
My second favorite highway is Going to the Sun....not all that far from Yellowstone and western Montana is beautiful.
On edit: Yellowstone itself is spectacular and don't miss it but the crowds and campgrounds start to wear on you after awhile. I get up on the Beartooth and I can start to breathe again. Good camping, both dispersed and FS on the southern side before the summit.