Bumping on Overbooked Airplanes Requires Dealing Fairly Act or the BOARD Fairly Act This bill directs the Department of Transportation to modify a federal regulation relating to oversold flights to ensure that an air carrier: may not refuse to transport a passenger holding a confirmed reserved seat on a flight to provide a seat for another passenger, regardless of whether such passenger is an air carrier employee; negotiates and solicits a volunteer to relinquish his or her space before boarding the aircraft; and if necessary, continues to increase the amount of compensation offered until a volunteer willingly accepts the offer in exchange for relinquishing a confirmed reserved seat.