I suggest you take US 301 from Richmond, VA across the Potomac River bridge and avoid driving in the Washington, DC area. It can (almost always) be a real mess and very slow traffic depending on the time of the day. Avoid rush hour.
You can catch US 301 from I-295 in Richmond. If you are afraid of narrow bridges be prepared for the Potomac River bridge. It is narrow, but big trucks & large RVs take it all the time.
I 2nd the suggestion to stop at South of the Border (NC/SC on I-95) and spend the night there in their campground. Easy in/out and reasonable price.
Have fun.
