Well, it isn't all done yet, but when it is complete, the Met Branch Trail will take you all the way from Union Station up to Silver Spring. I think there is an interim trail that is recommended until they actually finish everything, so you might want to check that out.
http://www.metbranchtrail.com/map.html
I recently moved from Capitol Hill to Arlington, which extended my commute to Adelphi, MD by a good 5 or 6 miles one way. My first approach was to try renting a bike locker at the NY Ave Metro and just riding from there. That was quite doable (and cheap, at $75/year for the rental), but I found fairly quickly that I actually preferred to ride the whole way. I may start using the bike locker again when it gets cold, but for now, I am really enjoying the longer ride most days. I also found that I can ride the 18 miles faster than I can take the metro/bus combo I would have to do otherwise. You might think about renting a locker at the new bike station next to Union Station. That way, you could ride from home to Union Station and then metro from there on to SS. It is definitely a manageable commute, though. Good luck!