The Museum is easily reached by bike on the beautiful lakefront path, just across Lake Shore Drive from the Museum. (From downtown, the ride is approximately eight miles.) Just north of 57th Street, follow the ramp down into the underpass below Lake Shore Drive, then left into the underpass below 57th Street. The Museum's main entrance will be ahead and to your right. Bike racks are available on either side of the main entrance.
To find other routes, find your starting point on the City of Chicago's bike map. The detailed section showing the Museum is here.
One bike option great for both Chicagoans and visitors is Divvy, Chicago's bike sharing system. Divvy offers both annual memberships and 24-hour passes for unlimited 30-minute bike trips. Just unlock a Divvy bike at the station nearest you, then dock it at the Divvy station just outside the main entrance to MSI. (For lakefront riders who want some extra time getting here from downtown, the 31st Street Divvy station is a convenient point for docking and undocking your bike to restart the 30-minute timer.)