Catalytic bimetallic Janus particles swim by a bipolar electrochemical propulsion mechanism that results from electroosmotic fluid slip around the particle surface. The flow is driven by electrical body forces which are generated from a coupling of a reaction-induced electric field and net charge in the diffuse layer surrounding the particle. This paper presents simulations, scaling, and physical descriptions of the ex- perimentally observed trend that the swimming speed decays rapidly with increasing solution conductivity. The simulations solve the full Poisson-Nernst-Planck-Stokes equations with multiple ionic species, a cylindrical particle in an infinite fluid, and nonlinear Butler-Volmer boundary conditions to represent the electrochemical sur- face reactions. The speed of bimetallic particles is reduced in high-conductivity solutions because of reductions in the induced electric field in the diffuse layer near the rod, the total reaction rate, and the magnitude of the rod zeta potential. This work suggests that the auto-electrophoretic mechanism is inherently susceptible to speed reductions in higher ionic strength solutions.