If you ever had any thoughts about being in DC for any major event, biking through DC while traffic is a near standstill is just awesome! Not to mention participating in the events themselves.
A bike route from Baltimore to DC: https://bikewashington.org/routes/dc2balt/index.htm
I’ll note the above site has other "invasion" routes to DC if you happen to live somewhere else near DC.
The inauguration is Monday, January 21. https://dc.about.com/od/specialevents/a/Presidential-Inauguration-2013-Washington-Dc.htm
The Washington Posts article about this: https://www.washingtonpost.com/local/trafficandcommuting/for-many-biking-is-the-sane-way-to-get-to-inauguration/2013/01/14/f247bc3c-5b6a-11e2-88d0-c4cf65c3ad15_story.html
Biking in Baltimore