I just found a listing for his grave in the book: Union County, North Carolina Family Cemeteries by Otha B. Small, 1992. This is what it says:
Bivens Family Cemetery, located on the Old Nathaniel Bivens Property, now owned by Faye Bivens Giles, a descendant. Copied by Charles F. Bivens.
Bivens, Margaret Oct 4, 1793 - Dec 14, 1859
Bivens, Nathaniel Nov 18, 1787 - Nov 14, 1845
Six additional markers with no information.
Maybe someone reading this can help you locate the exact location of the property.