When I make that trip, I usually stay on Hwy 2 to Shelby, then take I-15 to Helena, then Hwy 287 to I-90 and then to Bozeman and Billings.
I like to use freeways whenever possible.
I have also been known to go to Kalispell, then take Hwy 93 to Missoula, then I-90 to Bozeman and Billings.
Nearly any combination of state, federal, and interstate highways can be done in a large RV.
Remember that if you have 4 or more vehicles trapped behind you, state law requires that you pull off where it is safe and allow them to go by.
Have a safe trip.