The campground at Missouri Headwaters State Park [1] (four miles northeast of Three Forks on Road 286, 406/994-4042, http://fwp.mt.gov/parks/ [2], May 1–Sept. 30, $12 camping fee includes day use) has brushy riverside sites perfect for those on a Lewis and Clark pilgrimage. Read their journals first if you doubt the importance of bringing mosquito repellent.
There’s also a large state park campground (with showers) at Lewis and Clark Caverns (19 miles west of Three Forks on Hwy. 2, 406/287-3541, http://fwp.mt.gov/parks/ [2], $15 camping May–Sept., $13 Oct.–Apr., $40 cabin May–Sept., $25 Oct.–Apr.).
From Norris, about 30 miles south of Three Forks [3], head east on Highway 84 for nine miles to find Red Mountain (406/683-2337, www.blm.gov/mt/ [4], May–Dec., $8), a Bureau of Land Management campground near the bridge over the Madison River.
For a secluded spot, try Potosi (about eight miles south of Pony, 406/682-4253, June–Sept., free).
Links:
[1] http://www.moon.com/destinations/montana/the-missouri-headwaters-and-south-central-montana/three-forks-and-the-madison-river-/missouri-headw
[2] http://fwp.mt.gov/parks/
[3] http://www.moon.com/destinations/montana/the-missouri-headwaters-and-south-central-montana/three-forks-and-the-madison-river/three-forks
[4] http://www.blm.gov/mt/