I've done a similar style trip the last two years. Flew in and out of Bozeman, rented a car, and fished the Gallatin, Madison, Lamar, Soda Butte, Lamar, Slough Creek, Yellowstone, and Boulder River. If you don't mind roughing it a bit, I recommend bringing camping gear with you. You can camp for dirt cheap right on the bank of most rivers. I figure that if I skimp on lodging I can afford a float trip one day of the trip.
If you decide to try this area, let me know and I'll give you some tips on places to stay, fish, and eat, including the source of the best jerky in known to man.
Good luck and have fun planning your trip. I have nearly as much fun planning a fishing trip as I do when I actually go.