There's a monument tour that starts out of Union Station, if I'm not mistaken. They will rent you a bike and you go on a guided tour, so they make sure you stay safe. I think it's geared toward the tourist crowd, and I believe they do sessions at night, too, which would be a real treat.

Here are some helpful websites that are great info sites for cycling in the DC area:
www.waba.org
www.bikepptc.org
www.wodfriends.org

I hope you fly into Reagan instead of Dulles. The descent is just incredible. You also can probably take the metro to your hotel.

ENJOY!!