I rode through Yellowstone last summer, from my home in the Sacramento area. I rode to Carson, WA, and along the Columbia River, and up to Randle. From there I took Highway 12 through Idaho to I-90 in Missoula and slabbed it to Butte. The ride from Carson to Missoula was memorable and I'd highly recommend it.
If you were to head over to the east side of Yellowstone, around Cody as dbw suggested, there's also some great riding to do in and around the Bighorn Mountains. Highway 14 between Grey Bull & Ranchester is also a treat.