IM(H)O: No. Rt 28 is 4-lane limited-access, doesn't mellow until south of Manassas. 29 is almost as bad (4-lane all sorts of strip malls and side streets) until after Manassas.
Check bikewashington.org and bikepptc.org for routes heading towards Charlottesville.
http://www.bikepptc.org/cue_sheet_library/#VIRGINIA They have a bunch of rides starting in Nokesville (just SW of Manassas) which is at least in the correct direction. A query on their mailing list would likely turn up local info if you can get on it before you need to leave tommorow.
The Washington & Old Dominion (W&OD) trail heads west from near East Falls Church and West Falls Church metro stations to Purceville VA. (note no bikes on Metro during rush hours). Or start in DC on the Custis Trail in Rosslyn and connect to the W&OD. Takes you out of the ways north but once out there, you can head south on back roads.
http://www.bikewashington.org/trails/wad/wad.htm Trails End Bikes in Purceville - right at the end of the w&od - may have some suggestions; 540.338.2773.