Go for it. Ride as close as you can, then park the bike in the best place you can find. This is going to be a unique event, and you cannot predict or plan how it's going to go; so wing it.
I used to live in DC. I was 15 when, one inauguration day, my father said, hey, why don't we go down there? It was a warm day, and the ceremony had already begun, but we figured, what the hey? Drove down and parked somewhere on North Capital, near the GPO, and walked from there. Found ourselves a spot to stand on Constitution Avenue, and just a few minutes later Jimmy Carter came by, on foot, waving and smiling. Definitely the proudest day of my life until that point!
I took my first train ride ever to the JFK Inauguration from Philadelphia. Went in a passenger car full of paperboys who earned the trip as prize for selling so many new subscriptions for The Evening Bulletin. It sure was cold.