If you are just wanting to make time and go the quickest way, then over Teton Pass through Driggs to Idaho Falls and up I-15 - then west on US 2 and up to Browning, take the "Duck Lake" cut-off just as you enter town which brings you out to US 89 south of Babb (which is the entrance into Many Glacier) and you would turn left, or south, to get to Johnson's at St. Mary. You could make it in one day.
If you are going to Canada, don't forget your passports. If you are taking your time and making the trip between the two, as part of your vacation, that's a completely different answer. If that's what you're asking, how many days do you want between the two? Oh, and the airport in St. Mary is actually closer to Babb... if that's what you meant in your post!
1976 Airstream Overlander International