Southwest Montana rocks. We did a nine day loop tour out of Missoula this summer. This was the planned route (clockwise):

http://www.bikely.com/maps/bike-path/BIG-SKY-LOOP

We kept the mileages relatively low so we could have some time to relax. Unfortunately, we had to make a substitution for Philipsburg to Hamilton near the end of the trip because Skalkaho Pass was closed due to a washout. You could easily expand/modify this loop to include Bozeman if you have two weeks. For example, you could head west from Bozeman to the junction of MT 2 and MT 41 and pick up our route over Pipestone Pass to Butte. On the way, you could stop at Lewis & Clark Caverns on MT 2 east of Whitehall. Go over Skalkaho (MT 38) to Hamilton as shown on the map and then make the turn towards Darby (The part between Hamilton and Missoula is the least interesting.) When you get to Twin Bridges take MT 287 through Virginia City to Ennis. The view of the mountains from the scenic view area on the descent into Ennis is amazing. From there, head northeast back to Bozeman.

We found Montana to be pretty cheap. There is no state-wide sales tax, which helps. Lots of camping opportunities, especially in the national forests. The areas where we rode, except for in and around Butte, had little traffic. Drivers were very friendly and courteous. On one dusty road, an approaching pickup truck actually stopped for 2-3 minutes so we wouldn't have to ride through his cloud and then waved as we passed. You can ride on any Interstate if you want. Wildlife is abundant. We saw, among other critters, countless deer, a moose with her calf (also just missed seeing three other moose), sandhill cranes, a bald eagle and several dozen pronghorn antelope.

One nice feature is that you can design a trip that has both mountains and valleys so you are not spending every mile climbing or descending. I highly recommend the whole Lost Trail/Chief Joseph Pass thing along with the Pioneer Mountains Scenic Byway, both of which we did. And the town of Twin Bridges has a fantastic cyclsist-only campground right along the river.

Here is a slideshow from the trip:

http://www.youtube.com/watch?v=F7-k2ZMFL_I

I have toured in/through the state three other times. I have always loved it. The one thing you will have to put up with to some degree is the dreaded mosquito. This summer was really bad, even by local standards. Lots of snow over the winter means lots water come spring. They are usually only a problem in the early morning and evening.

Send me a PM with any questions.