A method and system for lifting drilling mud from subsea to a drilling vessel includes a pump having a body with a chamber, and a bladder in the chamber. The bladder spans the chamber to define water and mud sides in the chamber. A mud inlet valve allows mud into the mud side of the chamber; which moves the bladder into the water side and urges water from the water side of the chamber through a water exit valve. Pressurized water enters the chamber through a water inlet valve, which in turn pushes the bladder and mud from the chamber through a mud exit valve. The bladder separates the mud and water as it reciprocates in the chamber. A pressure control circuit equalizes pressure across the water valves, and a control valve provides a back pressure in a discharge of the pressure control circuit.