We rode Yellowstone, from Gardiner southeast to the Grand Canyon before joining the TransAm at Lake Yellowstone, last September. We found little traffic in the park, especially up north. We did ride in the rain for 2 days from Dunraven Pass to Moran, so this may have decreased the traffic in the south end of the parks. The riding was beautiful, with the really vibrant colors (fall colors starting to come out too). Food in the park is expensive, so I suggest packing your own as much as possible.

Every park campground has hiker/biker spots for discounted rates. The Park Service has a policy of NEVER turning away a hiker or biker, so you'll find camping options at every stop. The folks at the Flagg Ranch Lodge on the west side of the Rockefeller Parkway just south of the Yellowstone south entrance are really great. We showed up in their upscale lodge cold, wet, and dirty and they sat us down in the dining room for a reasonably priced dinner and treated us really well. As a result, we stayed in their campground a few hundred feet from the Snake River. The next morning, it was 22 degrees when we woke up and we returned to the lodge's beautiful stone fireplace and ate cinnamon rolls from the lodge store and dried our shoes. Really great folks there.

As far as bears are concerned, a couple of the campgrounds we stayed in had seen bears recently, but not during our stays. Never eat near or in your tent (be mindful of cooking smells blowing across your tent, as well. Take a set of non-eating clothes and keep your eating clothes with your food stash. You should be fine.

I'd be just as concerned with bison on the road. You'll feel much more exposed on your loaded rig than the gawkers in their cars. We found a ton of bison on the road near 3 Falls and south of the Grand Canyon.

Brian

edit: There were bear boxes at every campground we stayed in in the parks.