Mountain biking the backcountry roads can be so solitary that you're unlikely to encounter another human being. However, the solitude also means you should be extraordinarily prepared for the unexpected with ample supplies, especially water and sun protection (summer heat is brutal, and you're unlikely to find shade except in forested areas of Chisos Basin). Biking is recommended only during the cooler months (October–April).
On paved roads, a regular road bike should suffice, but you'll have to bring your own—outfitters tend to stock only mountain bikes. Off-road cycling is not allowed in the park. For an easy ride on mostly level ground, try the 13-mile (one-way) unpaved Old Maverick Road on the west side of the park off Route 118. For a challenge, take the unpaved Old Ore Road for 27 miles from the park's north area to near Rio Grande Village on the east side.