If you want to ride Yellowstone you need to set up a guided trip. Probably best to just set something up with one of the many tour folks. Since only 4 strokes are allowed, and only ones that are B.A.T.( Best Available Technology) certified. Which usually means current model year machines.
Jackson is a great place to stay, if you bring your own machines set up a reservation at Togwotee Mountain Lodge, can stay and ride right out of the lodge.