I’ve ridden Bike Route 1 in Richmond, and the linked article correctly describes it as well marked (and it’s quite pleasant). I do not think the same is true for BR-1 from here to Fredricksburg. In fact, if I’m recalling things correctly, one of the more serious vehicular cyclists I know described BR-1 through Prince William County as a mess. So I’d beware relying on its designation as BR-1. Depending on the kind of bike you’re on, you might want to look into incorporating the Cross County Trail into your plans (that’s also not very well signed, but I understand that the trail itself is pretty good).
If you come back with a map, I suspect you can get some good feedback. Good luck.