Bar Removal of Individuals who Dream and Grow our Economy Act or the BRIDGE Act This bill amends the Immigration and Nationality Act to provide that the Department of Homeland Security (DHS): (1) shall grant a three-year provisional protected presence to a qualifying alien, (2) may not remove the alien from the United States unless such protected presence is rescinded, and (3) shall provide such alien with employment authorization. An alien is eligible for such protected presence and employment authorization if the alien: (1) was born after June 15, 1981; (2) entered the United States before attaining 16 years of age; (3) continuously resided in the United States since June 15, 2007; (4) was physically but unlawfully present in the United States on June 15; (5) on the date the alien files an application the alien is present in the United States, is enrolled in school or in an education program assisting students in obtaining a high school diploma, has graduated or obtained a certificate of completion from high school or a general educational development certificate, or is an honorably discharged U.S. Coast Guard or Armed Forces veteran; (6) has not been convicted of a felony, a significant misdemeanor, or three or more misdemeanors not occurring on the same date and not arising out of the same act; and (7) does not otherwise pose a threat to national security or a threat to public safety. The bill: (1) provides for confidentiality of application information, with certain national security and law enforcement exceptions; and (2) sets forth the criteria under which DHS may rescind protected presence. An alien granted protected presence is not considered to be unlawfully present in the United States during such period. An alien must be at least 15 years old, unless in removal proceedings, to apply for protected presence. DHS may provide for an application fee and for fee exemptions. DHS may not: (1) remove an alien who appears prima facie eligible for protected presence while the alien's application is pending, or (2) refer individuals whose cases have been deferred pursuant to the Deferred Action for Childhood Arrivals Program (DACA) or who have been granted protected presence to U.S. Immigration and Customs Enforcement. A DACA alien is deemed to have protected presence through the expiration date of his or her deferred action status.