Always wanted to do that one. I've hiked it, but not gotten there with a bike.
I have ridden it from the top of Skyline Drive all the way to MM469 and back. It's a great ride, well worth the time and effort. Grab your bike and come on out, I'd be happy to ride with you. There are a lot of great trails and sites along it. Mabry Mill is pretty cool. The main visitor center usually has live folk music in the summer. Linville falls has some great views. Plenty of places to camp along the way, too. Right now is the best time of year for it, since the humidity isn't in full effect. Once the humidity gets thick, the views aren't as majestic -- nice humidity haze. Mid to late fall is great, but sometimes chilly and you miss out on the musicians and blacksmiths and such that reenact the old days at some of the sites.