A bearing for a wellbore tool includes a flow device. The flow device may be a pump such as a positive displacement pump or a hydrodynamic pump. In arrangements, a pump stator connects to a wellbore wall. A pump rotor rotates with a drilling motor, and/or a drill string. Rotation of the pump rotor may generate a pressure differential to displace the fluid. The pump may be configured to flow fluid across a gap between a rotating section and a non-rotating section of the bearing. The fluid may be drawn from a wellbore annulus and also returned into the wellbore annulus. The bearing may support thrust loadings and/or a radial loadings. In embodiments, inserts in the bearing may be used to filter the fluid.