I travel from just west of Charlottesville to southwest of Lynchburg every week to camp at my seasonal site. I am pretty familiar with the area you are speaking about. The problem is that there is a mountain between Lynchburg and Natural Bridge and unless you travel north of Lynchburg to go across it on US 60 or south to go across it on US 460, you're traveling over roads that are less than US routes and may cause you issues. This map might shed some light on it for you - it's Virginia's truck routes map -
http://vatruckweb.vdot.virginia.gov/VaTruckRestrictions.aspx
