I'm not sure about bikeabilty in and out of the base, I've biked to Anacostia Park which is near the base and there is a sidewalk along the bridge that can be biked (a bit narrow in spots but everything else is doable on a bike. You may want to look at Google's bike directions, while still in beta it does show trails and (some) bike routes in the area. You may also want to try asking on
http://groups.yahoo.com/group/BikeWashingtonDC/