The hydrodynamic interactions of a swimming bacterium with a neighboring surface can cause it to swim in circles. For example, when E. coli is above a solid surface it had been observed to swim in a clockwise direction. By contrast we observe that, when swimming near a liquid-air interface, the sense of rotation is reversed. We quantitatively account for this through the hydrodynamic interaction of the bacterium with its own mirror image swimming on the opposite side of a perfect-slip boundary. The strength of the coupling is reduced for longer cells, where the torque is spread over a larger length, resulting in longer bacteria swimming in larger circles. We confirm this through precise video measurements of bacterial trajectories and orientations.