While mountain biking inside of Yosemite National Parks is not allowed, there are some great options just outside the park boundary. Trails on the Eastern Sierra side, near the Tuolumne Meadows entrance, offer the best scenery and singletrack. Two great biking options are Bennettville Trail and Saddlebag Lake Trail.
Bennettville Trail follows a section of the historic Great Sierra Wagon Road and scenically weaves past the infamous mine, the Great Sierra Tunnel, on its way to the ghost town of Bennettville.
Nearby, the Saddlebag Lake Trail is a mountain bike blessing. Absolutely amazing high sierra scenery surrounds this loop, which is nestled between Hoover Wilderness and Yosemite.
Another ride in the area, Lake Canyon Trail, requires a bit more aerobic exertion. Details and maps of the ride are depicted in Mountain Biking Mammoth. Enjoy!