Glad to hear you may be stopping here in Asheville. There are lots of options available and I am happy to tell you what I know about any of them if you want to PM me any questions about other parks.
In looking at your criteria of a place to spend the night and to leave your trailer for a few days and to be accessible to mountain biking, my first recommendation would be Taps RV Park
. It by no means is a luxury park, but is clean and quiet and safe for a quick nights stay. from her you could literally ride your bike to the Blue Ridge Parkway
without moving your TV.
It is located just off exit 55 in east Asheville and is an easy off/on. I think their rates are reasonable as well.
Similarly there is the KOA East Asheville
which is ok as well. Neither of these have lots of amenities but that did not seem to be what you were looking for.
If you are looking for the pool and other RV "resort" type things I would suggest. Bear Creek Rv Park
. It is located in West Asheville very close to the Farmers Market
, but does not have the same mountain biking locations a close by.
If you can pull a short distance from I-40, I would suggest Lake Powhatan
Campground. It is a state park and has a very woodsy feel. The sites are great and do not tend to back up to each other so closely. Roads are paved and sites are concrete pads. Very nice place. I do not know that they would allow you to leave your trailer there while you were gone, but you could ask about that. It is very close to the Bent Creek
recreational area that has lots of mountain biking trails. you could ride for days and not cover them all.
I hope this is helpful.
Let me know if you find other places that you want to know about. This is only a short list of ideas off the top of my head.
Don't know if you are into this sort of thing or not, but we have a wonderful selection of locally brewed beers. We are after all Beer City USA
and I have not even touched on the local food available. I can make recommendations on that later if you would like.