A pump includes a pump body and a pump bulb that is connected to the pump body, an inlet valve assembly, and an exhaust valve assembly. The pump bulb is operable to move fluid between the reservoir and the cylinder. The inlet valve assembly includes a valve and a tubular sleeve that provides an exit valve seat. The inlet valve assembly is operable to allow a portion of fluid to be drawn from the reservoir through the tubular sleeve and through the inlet channel for delivery into the pump bulb. The exhaust valve assembly is operable to allow the portion of the fluid delivered into the pump bulb to be moved into the cylinder. The valve is movable to contact the exit valve seat and prevent fluid that is flowing from the cylinder to the reservoir from flowing through the inlet channel.