TL;DR: Do not attempt to bike around or through the federal core of DC for the next week.
Things to know:
Bicycles are not permitted within the Inauguration Perimeter.
The Secret Service has not released a full map of closures, but there’s a list: lots of roads and bridges are closed. The Memorial Bridge and 14th Street Bridge are currently listed as open to pedestrians, but we do not recommend relying on that, and would definitely not plan to try to bring your bike with you.
As of this writing The Google Maps traffic layer has reasonably current closures marked.
Trails are not included in the closures lists we’ve seen, but assume that portions of the Rock Creek Trail around the Kennedy Center will be closed, and probably sections of the Anacostia River Trail between the 11th Street Bridge and the Jefferson Memorial.
Some brief editorializing:
In a normal inauguration year, we would be recommending your bike as a great way to get close to the National Mall without dealing with parking or crowded trains.
This year, there will be violent fascists around the city looking for a fight and an on-edge security apparatus looking to stop them.
Stay safe. Stay home if you can.
If you’re getting on your bike for fun, head away from the city rather than toward it.