I don't live near there, nor have I ridden there, but a quick look at a "google-earth" app, I immediately was drawn to 622, 626, and 708. Essentially paralleling US-29.
But if you just bought that bike, and haven't been cycling, you might want to start with a route(s) that are more circular, and don't get so far from home -- in case you have trudge home because you are exhausted, or in case you are too tired to even trudge, and need to call for a "rescue".
Cycling is easy and fun. But the easy and the fun does take some conditioning and getting used to -- esp. if one lives where there is as much UP and down as around Lynchburg and Charlottesville.