I have no real allegiance or affiliation to any of the shops in town. Nor do I know for sure if any will do that type of thing but I suspect any of them would. For me easy access from the interstate and the airport would probably be as big of a factor as any. So this may depend on where you planning on ridding or staying. In no particular order.
http://carolinafatz.blogspot.com/ Great shop and the staff has always been super helpful and knowledgeable. Pretty easy access from the interstate and right next to Bent Creek
http://www.motionmakersbikes.com/ I'm not the biggest fan of Specialized and they are kind of the new kids on the block, right up the road from Carolina Fatz, while they didn't have the part I was needing(none of the other shops in Asheville did either) they went out of their way looking for the part and seeing if they could order it.
I'll mention Pro Bikes since I know that they go out of their way to help out of towners. I know the owner sized/fitted a tourist then delivered a rental to the hotel.
http://www.pro-bikes.com
In all honesty I don't have anything negative to report about any of the shops in Asheville, but the ones listed are all straight shots of the interstate.
PS I want to travel out your way this summer, though I don't think it will happen this year. I flew out to Jackson WY last summer with more backpacking and fishing gear than 2 bikes weigh and it wasn't cheap. I just shipped it UPS general pickup, luckily I called the day before in because apparently Betty, the person who was supposed to be manning the station, was having a baby and wouldn't be in that day. They arranged for someone to be there, umm thanks. Anyways that is always an option, I'm not exactly sure where the UPS general delivery pick up is but the Fedex is right off the interstate and close to downtown.