BARR Preservation Act of 2011 - Directs the Administrator of the Federal Aviation Administration (FAA), upon request of a private aircraft owner or operator, to require that, with respect to that owner's or operator's noncommercial flights, the display of the owner's or operator's aircraft registration number is blocked in aircraft situational display data available to the public. Allows the Administrator, however, to make such information available to federal, state, or local government agencies.