I live in South Carolina also. This state is by a mile the easiest state to set up a camp without problems. The one exception are friday nights in the fall where hunters will be everywhere so be careful about staying away from areas that have evidence of recent human activity.
An excellent site for SC bike routes is
http://www.sctrails.net/TRAILS/ALLTR...de/biking.html
On that link, they even talk about bicycle camping including impromptu camping.
Happy touring!