I live in Potomac near where Montrose and Falls intersect, and commute by bike to DC every day (17.5 miles each way). If you can get to Wooten Parkway it is a safe commute. Wooten Parkway to Falls. Falls south to Tuckerman. Tuckerman to Seven Locks. Seven Locks to Bradley Blvd. Bradley to the Cap Crescent Trail, which will take you straight into Georgetown under the Whitehurst Freeway.
You might want to avoid Falls and go through a neighborhood behind Wooten High School to Falls Chapel, which will take you straight to Tuckerman. All bicycle friendly roads with paved shoulders.