For camping and all types of lodging info on any location in Montana, a good website is: http://visitmt.com/tripplanner/campandlodge/
Here are some of my ideas for Bozeman lodging including prices. I picked them based on my own judgment with no intention of getting business for a particular place. You might find other places more suitable and you can probably talk most of these places into discounts. Bozeman is small enough where time to the race start from any particular lodging is not a consideration unless you count an extra 10 minutes of sleep as valuable. For example exit 305 at N. 19th is closest to the Jim Bridger races, at about 12-15 minutes. The cheap places and center of town add about 5 minutes but are closer to the Devil’s Backbone. Exit 306 is closer to the Bridger Ridge Run. I asked for summer prices for a single/double. Camping in the National Forests is possible at Battle Ridge on the east side of the Bridgers, and several places up Hyalite Canyon, (Hyalite is very close to the DB but usually very full in July). A pretty place is out in the Spanish Peaks at S. Fork of Spanish Creek (an hour away from all races).
Hostel where you share a room is in mid-town. 406-586-4659. $18/person. One private room with a queen bed for $34. Call well in advance or email Scott bozeman4hostel@yahoo.com .
Blue Sky Motel on E. Main near exit 310 is a small row-like set of rooms like you see along highways everywhere, older and accept pets. 800-845-9032. 2 queen beds for $61. One person $49.
Imperial Inn is right in the center of town on Main and Grand, handy to eateries and town-life. Several stories with porches outside to access the upstairs room. What I call a Motor Inn. Old but well-maintained. 406-586-3354. 2 queen beds for $75. One person $65
Lewis and Clark on Main and 8th is similar to Imperial Inn but more towards the edge of town. Indoor pool, breakfast 800-332-7666. 2 people - $75, 1 person $65.
Super 8 is back on the Interstate again, near exit 307 at N. 7th. Typical Super 8 with a McDonald’s right next to it plus a pretty good all-you-can-eat oriental buffet. Breakfast. 800-800-8000 (ask for Bozeman). 2 people $73, one person $63.
Best Value near exit 306 at N. 7th. Like Super 8 but with pool, breakfast. 406-585-7888. 2 people $65, one person $60.
Classier is the Best Western Grantree Inn on N. 7th near exit 306, 800-624-5865. Pool, breakfast. 2 queen beds for one or two people is $111.
Marriott Fairfield Inn on N 7th near exit 306. 800-228-2800. Pool, breakfast. 2 queen beds for one or two people is $89.
Wingate Inn on N 19th near exit 305 (closest to the race). 800-228-1000. Johnny Carino’s Italian next to it. Pool, breakfast. 2 queen beds for one or two people is $109.
KOA Campground at Bozeman Hot Springs which is 9 miles west of town, 15 minutes further from the interstate but a great hot springs pool, etc. $26 tent site. 800-562-3036.
Sunrise Campgrounds, close to the interstate with attendant noises. 877-437-2095. Tent 1 person $12, 2 people $15. RV prices too.
Bear Canyon Campground, above the interstate so quieter. $16 for two people in a tent. 800-438-1575. RV prices too.