There are picnic facilities at the lower parking lot along the river, but camping is not allowed. The closest services are in Wisdom [1], 10 miles east. May Creek Forest Service campground (406/689-3243, www.fs.fed.us/r1/b-d [2], July–Labor Day, $7) is eight miles west on Highway 43.
Links:
[1] http://www.moon.com/destinations/montana/butte-helena-and-southwestern-montana/the-big-hole-river-country/the-big-hole/wisdom
[2] http://www.fs.fed.us/r1/b-d