not familiar with any group rides, but there are a lot of good palces to ride. One good ride is up past the Grove Park to Town Mountain Road, then north on the Parkway(bring lights for the tunnels, small blinkies are enough). From there to the Visitor Center is one almost continuous climb of 30 miles. You can go further and turn up Mount Mitchell.
There's a ride that starts up the same way, then drops down Oxbow, and makes a loop along the French Broad River, which is a good 30-40 miles.
Find the book Road Bike Asheville, and there a number of routes.
http://www.amazon.com/Road-Bike-Ashe.../dp/1889596000