I live in Buffalo and can give you more detail.
US 16 is far preferable to riding I-90 - albeit about 33 miles longer.
Services are available at the Spotted Horse bar - all you really need including camping.
Then Arvada is at the Powder River a mile off the road - with bar and camping, if nec.
Leiter is further down the road with water and food if the restaurant is open - - iffy.
Next is Clearmont - a small town with store - you can beg to camp in the park.
Finally there is U Cross - the Art Foundation is open to public with restrooms, water.
My suggestion is to camp at Clearmont -
Then ride in the morning with the sun illuminating the snow-capped Bighorn Mountains.
Climbing the Bighorns is not for wusses.
Although the elevation gain between Buffalo and Powder River pass is 5000 feet -
The actual climbing is more like 7500 feet because of 7 ridges.
The Bighorns do have the most spectacular wildflowers in the West in late June/early July.
Plan to spend a night up top - but plan to be chilly.
Then Tensleep Canyon is eye-popping.
I suggest Nowood Valley to Manderson, then Basin, Arlington, Cody