I obviously have considered flying but Amtrak was suggested or the greyhound bus with stops on the way. I would love to get more feedback if anybody knows the best thing to do.
Fly. Pay the extra amount. Fly into Bozeman if possible and head to Yellowstone National Park - one of USA's true jewels.
I'd have to recommend flying. It might cost extra, but at least you're not losing days of your time.
I was in Missoula last February and it was magical. Highly recommended! If you're looking to travel throughout Montana, then perhaps the bus is a great thing to consider.