Hi,
I found a very nice, if roundabout route from Missoula to Bozeman a few years back, in the summer of 2000. It was inspired by the fact that the place was burning, and I was trying to ride where the fires weren't.
Follow Route 200 out along the Blackfoot River, of "A River Runs Through It " fame. Stop off in the bar in Potomac and have one of the local brews, Moose Drool. Brush up against the side of the Bob Marshall Wilderness. Stop off at Loonie's; you can tell by the giant metal dinosaur sculpture and the Harleys parked outside. Pass through Lincoln. Out of town, turn right and climb: Flesher Pass over the Divide. Sweet, tough and lonely.
Roll down into Helena. Take the I-15 south of town - it's okay for riding - but watch out for a nasty unmarked pass coming up on Boulder. Be sure you have more than just a bottle and a half if it's a hot day. Turn off at Boulder and go south through the wild beautiful Boulder valley. If you're lucky, the rancher will let you camp by his corral and you can listen to the coyotes.
Keep south and cross I-90, heading down to Norris. Watch the rumble strips. They tend to disappear on the hills, only to reappear at the bottom right about when you're doing 40. At Norris, turn east to Bozeman.
It's been six years and I can remember each day vividly. Good luck and enjoy.