My friend who moved here from San Diego would drive by way of Las Vegas and St George, Utah and overnight in St George then home the second night. From SLC it is about a 7 hr drive to Bozeman if the weather is ok. Monida Pass is the one you always have to watch for coming from Dubois, Idaho to Montana state line. Then go to Dillon off I-15 and take the road to Twin Bridges and hang a left at the flashing light, go up the valley to I-90 and wave when you pass the big blue silos on Hwy 55 and get on the interstate at Whitehall and you will be 56 miles from Bozeman. By taking the cut off to Dillon, you cut off a big triangle from your drive. All the truckers take this route and you will save lots of time instead of driving all the way up I-15 to Butte and then across. Hope that all makes sense to you.
To lookup highway reports for Montana go to
http://www.mdt.mt.gov/travinfo/