The place to go for mountain bike rentals and information on area bike trails is BikeKraft (785 Rogue River Hwy., 541/476-4935, www.bikekraft.com [1]). They rent mountain bikes by the day or half-day. If you want to go on an extended trip, for a few days or a week, they can outfit you too, and car racks and trailers are available for rent; a cash deposit is required.
Other helpful resources are the Siskiyou National Forest Service (P.O. Box 440, 200 NE Greenfield Rd., Grants Pass, OR 97526, 541/479-5301) and the Bureau of Land Management (P.O. Box 1047, Medford, OR 97501, 541/770-2200).
Links:
[1] http://www.bikekraft.com