Depending on where you are in Rosslyn, I’d consider going around the Iwo Jima and either taking the Memorial Bridge or getting on the MVT after the Memorial Bridge (you have to cross the GWMP, which sucks, but you can see pretty well, and you get to avoid going under the Memorial Bridge on the MVT, which also sucks, but in a different way.
Depending on where you’re going on 5th St NW, I’d consider using the TR Bridge (if you can deal with it) and taking H to Penn in front of the WH then either NY Ave or Penn Ave to go east.
@dbb 179354 wrote:
I’d recommend down the Mount Vernon Trail to the 14th Street Bridge, around the Tidal Basin and up 15th Street to the Mall.
East on the Mall (Jefferson) and then north on 7th or 3d. Take a look at the DC bike map to see the route that works for you after you get north of the Mall.
You don’t have to play much in traffic until you get north of the Mall. Reverse (using Madison) in the afternoon.
dbb’s route was my first thought, with the caveat that Madison/Jefferson suck when there are lots of tourists (summer, Spring Break, particularly afternoons). When I had to go cross town for my commute, I would switch between Madison/Jefferson (in low-tourist season, mornings when I just felt like seeing the Mall) and Penn Ave cycletrack (when I didn’t feel like dealing with tourists).