Crystal structures of several bacterial Na(v) channels have been recently published and molecular dynamics simulations of ion permeation through these channels are consistent with many electrophysiological properties of eukaryotic channels. Bacterial Na(v) channels have been characterized as functionally asymmetric, and the mechanism of this asymmetry has not been clearly understood. To address this question, we combined non-equilibrium simulation data with two-dimensional equilibrium unperturbed landscapes generated by umbrella sampling and Weighted Histogram Analysis Methods for multiple ions traversing the selectivity filter of bacterial Na(v)Ab channel. This approach provided new insight into the mechanism of selective ion permeation in bacterial Na(v) channels. The non-equilibrium simulations indicate that two or three extracellular K+ ions can block the entrance to the selectivity filter of Na(v)Ab in the presence of applied forces in the inward direction, but not in the outward direction. The block state occurs in an unstable local minimum of the equilibrium unperturbed free-energy landscape of two K+ ions that can be locked in place by modest applied forces. In contrast to K+, three Na+ ions move favorably through the selectivity filter together as a unit in a loose knock-on mechanism of permeation in both inward and outward directions, and there is no similar local minimum in the two-dimensional free-energy landscape of two Na+ ions for a block state. The useful work predicted by the non-equilibrium simulations that is required to break the K+ block is equivalent to large applied potentials experimentally measured for two bacterial Na(v) channels to induce inward currents of K+ ions. These results illustrate how inclusion of non-equilibrium factors in the simulations can provide detailed information about mechanisms of ion selectivity that is missing from mechanisms derived from either crystal structures or equilibrium unperturbed free-energy landscapes.