Just west of Aspen, the Aspen Mountain ski area has a nice network of trails that are open to mountain bikes. Sadly, the lifts do not provide access to the trail system, so you better be ready to climb the Summer Road which has 3,500 feet of vertical over 5 miles to get to all the trails. But its worth it -- the descent is phenominal and you will probably be the only bikers on these trails. The main trail down is the Westside Trail, which sees little action and may be tough to follow at times. It's definitely a hardcore downhill route. Make sure to watch out for hikers.
The start of the Summer Road, which is a public access county road, is at the main Little Nell / Gondola base area.
If you get to the top and want to spin around alittle before heading down, try riding out the scenic Richmond Hill Road (aka Richmond Ridge). It rolls through dense pine forest and meadows offering occasional views of the surrounding peaks.