The Pendergrass-Murray Recreational Preserve (PMRP) is owned and managed by the Red River Gorge Climbers' Coalition (RRGCC) and does allow mountain biking on designated trails. The area is also the heart of a huge network of active and abandoned oil and logging roads.
Review: Trail was great for me and my 12 yr old- you'll have to walk at a certain point but it was gorgeous. Toughest part was the road getting to it. If coming from north stay on main roads as long as you can.