This door is the second door to get inside the room. I think it is a good idea to remove because if there is an emergency and it is the only way to get out, there will be a lot of trouble having to pass two doors.
Consider uploading photos, a short video, and a site plan drawing of the existing bike storage areas at your school.
City of Chicago Bike Program
The City of Chicago has lots of information about biking in the city. You can also learn about the Bike 2015 Plan to make biking an integral part of daily life in Chicago.