An apparatus for forming a wellbore in a subterranean formation includes a drill bit, a connector connected to the drill bit and configured to transmit torque and thrust to the drill bit, and a drilling motor energized by a pressurized fluid. The drilling motor may include a stator and a rotor disposed in the stator and having a torque transmitting connection to the connector. The apparatus may also include a thrust generator associated with the rotor and having a pressure face in pressure communication with a fluid flowing through the drilling motor and a force application assembly selectively anchoring the stator to a wellbore wall. A related method uses the apparatus to drill a wellbore.