Dear Gloriously Quit -
I like the glorious part.
When is you plannin' to do this?
You are aware that the Beartooth Hwy may not be open until July this year because of snow?
They got another 3 feet this week.
I agree with all those who suggest avoiding interstates - even service roads - esp railroad beds.
(I biked the old Milwaukee RR roadbed between Garrison and Missoula 20 years aog - bad idea.)
I'd head out on MT 200 to Ovando, then down on Helmville-Drummond County Rd to MT 1.
(There's only a short, hard-pack stretch.)
MT 1 is a nice ride to Anaconda - but you have to get on I-90 a little to get into Butte.
Then MT 2 (Old US 10) is a nice quiet ride over the Divide and down.
US 287 along the Madison River is sweet. W. Yellowstone - meh. US 20 - more meh.
From Driggs over Teton Pass is pretty busy - be careful.
Jackson - tourists by the millions and tourist prices.
There's a great, mostly paved Spring Gulch Rd between the two buttes into the park.
Absolutely, must take the Park Rd - Not US 89 - into Jenny Lake - Hiker/Biker camping.
Yellowstone can be a zoo - RVs galore.
South Entrance Rd narrow and busy.
Late or early - best time to ride - significant climb - shade.
If late, you can pull into Hiker/Biker sites at Lewis Lake.
(Much more pleasant than the carnival at Grant Village.)
Early, early morning on Yellowstone Lake is lovely.
Make sure to take the usually empty Gull Point Rd.
I prefer the South Rim of the Grand Canyon of the Yellowstone.
Them you can ride the old paved roadbed right before the river bridge.
(Technically illegal - but it's 16 ft wide.)
If they stop you ask them why they pave 40-ft pull-thrus
and don't allow bikes on the old road.
Then make sure to take the one-way Canyon Loop Rd.
Dunraven Pass is steep, narrow, with lots of tourists looking elsewhere.
Again, early or late riding avoids much traffic.
Tower/Roosevelt also has hiker/biker camping.
The Lamar Valley is a lovely, sweeping vista.
Unfortunately, lots of people line the roadway with cameras looking for wolves.
If the Beartooth Hwy is open, be aware that it can snow any time of year up top.
It is often exposed, often windy, and often cold.
Heading down the northeast side, check your brakes beforehand.
Stop often to let your brakes cool.
Take MT 78 thru Absarokee rather than Joliet Rd - partly unpaved - rough.
Personally, I'd take Rapelje Rd and the unpaved county road to Ryegate -
Rather than backtrack on I-90 and US 191. US 12 has fairly light traffic.
If you head towards Helena - you should take Hwy 284 on the east side of Canyon Ferry.
US 12/287 has brutal traffic and inconsistent shoulders.
Then rather than US 12, take Birdseye Rd and Hwy 279 over Flesher Pass.
Much, much nicer.
But if you don't want to come back to Mizzou via MT 200 -
You could always cut southwest from Townsend to Whitehall and Dillon -
Then follow the ACA route via Jackson and the Bitterroot Valley back into town.