Make lodging arrangements early and prepare to be baptised at least once a day.
Good that your trip is in June as a snow machine is the best way around that country in May.
Have good rain gear at the ready. Beartooth is a must and Sunlight basin too Cody is great but can be very windy. Avoid night riding as the deer, elk, antelope, ect move and feed at night.
Enjoy
Jim