In this paper, we address the problem of controlling an active magnetic bearing (AMB) with reduced ohmic power losses. A solution is proposed which introduces a "smart" bias flux in the nonlinear control law. The bias is smart in the sense that it is a function of the rotor states, and varies online in a manner that reduces AMB power losses and avoids control singularities without affecting the closed-loop stability. General conditions on the functional form of the bias are provided along with a specific bias design. A simulation study illustrates the performance of the proposed smart-bias controller in comparison to a standard constant-bias controller.