You absolutely want to take either interstate 15 or "
recreation road" between Helena and Great Falls. Recreation road is the frontage road to I-15, and the more twisty of the two. But the interstate isn't very straight there either, at least from Helena to about Cascade. Once north of there, both are pretty much parallel to each other. Recreation road ends at the Great Falls airport.
15 is the only way to get to the Great White North once you get north of Great Falls.
It's too bad that the Going-to-the-Sun road in Glacier National Park is a) closed until June, and b) too far out of your way, but if you ever come back, it and the
Beartooth Highway (also too far out of your way) are absolutely worth doing.
Depending on how much time you can afford to waste, traveling west from Bozeman all the way to Butte along I-90 (over Homestake Pass), then north on I-15 to Helena and Great falls is probably the most scenic option, with the real scenery coming in to view west of Three Forks (the headwaters of the Missouri River). Just north of Butte you'll cross the Continental Divide at about 6,800 feet.
About 15 miles north of Helena on I-15 you'll come across the Gates of the Mountains, so named by the Lewis & Clark expedition. The thing that amazes me is, we're seeing that area today largely the same way Lewis and Clark saw it.
Make sure your insurance is ok in Canada, and that you have a passport to get back IN to the USA.