These trails are only avaiable to people staying/visiting the Biltmore. there is a $5 charge payable at the outdoor center, except for those staying at the Biltmore Inn. The trails vary in difficulty and type from flat gravel/paved roads to some pretty sweet fast singletrack. The Arbor Trace trail and Black Diamond trail behind the Inn (Westover Trails) are fun and make a nice 90 minute ride. Access the lagoon trail from RiverBend farm and follow it right at the T intersection by the river, then just follow the trail and signs. Trails are well marked. Loop Arbor Trace through the trees, up some nice climbs and come back the way you came once you've done the loop past the farm. Then hit the Green trail as it runs up behind the outdoor center to the left and climb an access road and you'll see a sign leading to the black trail behind the old Chicken coop (reddish-orange clay building). There is also a green trail off to the right and a blue trail access of it, about a mile in. these are some cool trails; beginner to intermediate in nature. The black trail is label such because of some climbs and tight switchbacks, but pretty tame compared to DuPont, Bent Creek, Tsali. The green is rideable with a hybrid bike. HAVE FUN.
On the biltmore Estate, head to the OUTDOOR center. they have a great map that will outline all the trails, and the main trailhad takes off from behind and on front of the center.
http://www.singletracks.com/item.php?c=1&i=2629