Looks like you could dogleg off of Georgia onto Arkansas, take that to Piney Branch Pkwy, and get on Beach Dr/Rock Creek Pkwy down towards Georgetown. But I don't know what those roads are like for bikes on a Saturday morning, so I don't know whether it's a feasible option or not.

Since you ladies are riding, you decide. I'm driving because I'm planning to head up to Leesburg after our brunch, so these closures don't affect me.