In DC, the Washington Area Bicycling Association provides free bike parking for major events on the National Mall. I think they also have tried to make it easy to bike to baseball games and other events at Nationals Park, in terms of designated bike routes in the area and bike racks at the park. I honestly don't know how much these things are promoted to the general population.

Capital Bikeshare is very popular in DC and it continues to grow in the near-in suburbs, so I imagine people will use that to cycle to major events in the area.