Bruisin' Ales, Appalachian Vintner, and Tasty Beverage would probably all be about equal, adding a total of 10 miles extra. Hops & Vines is closer to the 26/40 intersection and would add a total of 5 miles. I haven't been to Hops & Vines though since I usually stick with one of the other three.
If I were you, I would divert the 5 miles and go to App Vintner. As @treznor said, you will have to divert to hit any of the bottle shops in Asheville
Stop at Sierra Nevada in Mills River just south of Asheville right at the airport and grab some growlers. It is a fabulous place. If it's the right time of day, the lunch menu is nice.