There is a $14 per car parking fee (2019) for cars entering the NC Arboretum unless you have an annual membership.
The trail starts about 1,000 ft into the arboretum from the trailhead just past the main entrance. This is the main "trail" through the park and very popular with hikers, strollers, dog walkers, etc. The trail is really more of a gravel road 6-8 feet wide although it narrows to a few feet after you leave the arboretum.
It follows Bent Creek the whole distance through natural forest occasionally with views but always with sounds of the creek. The manicured and curated collections are further up the hill and can be accessed using either Running Cedar Road
or Wolf Branch Road
. You'll have to bring a lock for the bike to visit the garden area though.
There is a gate at the property boundary, approximately 1.25 miles in, after which a narrower gravel trail continues on USFS property to the Bent Creek area. Both this gate and the vehicle gates will lock automatically when the arboretum closes each night.
There is also a Bent Creek Trail (singletrack) that parallels the road for part of the distance, but it is off limits to bicycles.