According to my mapping program (Delorme) you have two ways to get to Fishing Bridge and surprisingly, they are both the exact same miles of 1660. Amazing!
1. From Cincinnati take I-74 to I-80/380 to I-35 a short distance to I-90. At Buffalo, WY take 16 rather than 14 (an easier drive to Greybull) then 14 west into Cody and Fishing Bridge.
2. From Cincinnati take I-74 to I-80 to Rawlins, WY. Then pick up 287/26 into Dubois, WY continuing west into Grand Teton Nat'l Park then north to Fishing Bridge.
I would highly recommend that you allow a few days in Grand Teton Nat'l Park as it's completely different from Yellowstone in looks and in things to do. If you want hookups, Colter Bay RV is the one. If you can do without hookups both Colter Bay campground (right next door to the RV park) or Gros Ventre campground both have 300 non-reservable sites and if you plan it to get into the area in the morning you will have no problem getting a site. Gros Ventre is our favorite.
Since they're both the same distance, you could take one way there and the other way on the return.
Be sure to check out the park's web sites. They give lots of good information on what to do, the road information (sometimes there's repair issues), etc.
Grand Teton National ParkYellowstone National Park
