I come in from the other direction, but from your side, fwiw I recommend 15th St. It has a great bicycle lane from 16th St. (Columbia Heights) all the way downtown and is well travelled, but not car heavy.
Speaking of showers, does anybody have an idea if there will be showers at/near the Freedom Plaza pit stop tomorrow for Bike to Work day? I want to do a longer ride in, but know it will be a foul without a shower at the end…