Bicycling is permitted on established public roads, parking areas, and designated routes. Bikes are prohibited on backcountry trails and boardwalks.
Use extreme caution when riding on park roads; roads are winding and narrow while shoulders are either narrow or nonexistent. Vehicle traffic is heavy most of the time. There are no bicycle paths along roadways.
Yellowstone National Park has a great page on their website discussing cycling in the park. Be sure to watch the Park Service's video about cycling in the park as well. Just like in Grand Teton National Park, you can bike in Yellowstone during the spring before cars are permitted on the roads. Click here for more information about Spring Cycling in Yellowstone.