Welcome Ross the Lurker!
About the western parks -
There ain't no lodging for a 100 mile radius in mid-summer.
You are more likely to hit them in late June - still pretty over-booked.
But, if you do send camping gear out - then you have hiker/biker camping options.
In fact, then it becomes a cake walk getting overnight accommodations in the parks.
And in the most beautiful locations, too.
There is a fantabulous hiker/biker campground right on Jenny Lake in Grand Teton.
There are hiker/biker sites at all but one of the Yellowstone campgrounds. (Slough Creek)
BTW - I would strongly suggest a loop in Yellowstone that gives you far more of the park -
West Thumb > Bridge Bay > Canyon > Norris > Madison.
Canyon has hiker/biker sites both on the loop and deep in the woods.
Of course, with bears, some people prefer to stay on the loop, but the quiet of the woods is sweet.
Canyon also has showers, laundry, cafe, store, visitors center talks, and superb hiking.
One thing about sending camping gear ahead - you'll be a pro by Great Bend - with legs of steel.
Also, all the west Kansas towns have great hiker/biker camping often near the pool park.
Camping also makes sense once you hit the Rockies in Colorado - -
Although in can be pretty chilly in early June - just sayin'.
I have done both the I-90 route and the Hwy 200 route in western Montana numerous times.
Even though the rail trail system paralleling I-90 has been improved -
you still have to get on the Interstate a number of times or are right next to it.
I think the last of the bridges with zero shoulders and heavy traffic have been widened.
There are, however, some short stretches of Old Highway 10 that are lovely.
There are some stretches of Hwy 200 with no shoulder, but there is also much less traffic.
(You will have either a handlebar mirror or a helmet mirror - right??)
Camping at the fairgrounds in Plains is nice - big shade trees and showerhouse.
Then you take the bike/ped bridge acros the Clark Fork and up to Thompson Pass.
Thru Murray and on to Enaville and the Trail of the Coeur d'Alenes.
Great lakeside camping at Harrison.
If you do choose to follow I-90, I would suggest the Route of the Hiawatha Trail.
Incredible tunnels, long & high trestles, moderate grade, crushed limestone surface.
Then catch the last few miles of the Trail of the CdA from Haworth SP to Plummer.
May I suggest rideing thru the Palouse rather than south on US 95?
US 95 is really busy, usually with shoulders, but nothing to write home to Mom about.
The roads thru the Palouse are almost totally empty and like a magic carpet.
Plus, you could go via Palouse Falls when there is still quite a lot of water coming over the edge.
Pick Up the L&C at Walla Walla.
