I was wondering how this would go, so I'll share in case somebody else is wondering.
I rode on 28 for I'm guessing about 10-15 miles today. I just followed Google bicycling directions from Arlington to culpeper.
The first part of 28 is a pleasure. 4 lanes, divided highway, plenty of room and not much traffic (on a random Monday noonish).
Later on it gets to be two lanes, and at times the shoulder is slim to nothing. Even still, the traffic pretty moderate which made it tolerable. The beautiful scenery helped too!
I suspect riding it at not rush hour makes a difference.
Here are a few photos.