A bridge plug for use in a wellbore having an anchoring system to grip the inner surface of the surrounding wellbore, as well as a sealing system or packing element to seal against the inner surface. A hinged flapper permits flow of fluid in one axial direction through a central through bore, but can selectively contact against a seat to create a fluid pressure seal and prevent fluid flow through said central through bore in an opposite axial direction. The flapper can be manufactured of frangible material and/or dissolvable material, permitting selective removal of the flapper when desired.