The present work performed a comprehensive investigation to find the effects of a dual-bleeding port recirculation channel on the aerodynamic performance of a single-stage transonic axial compressor, NASA Stage 37, and optimized the channel’s configuration to enhance the operating stability of the compressor. The compressor’s performance was examined using three parameters: The stall margin, adiabatic efficiency, and pressure ratio. Steady-state three-dimensional Reynolds-averaged Navier−Stokes analyses were performed to find the flow field and aerodynamic performance. The results showed that the addition of a bleeding channel increased the recirculation channel’s stabilizing effect compared to the single-bleeding channel. Three design variables were selected for optimization through a parametric study, which was carried out to examine the influences of six geometric parameters on the channel’s effectiveness. Surrogate-based design optimization was performed using the particle swarm optimization algorithm coupled with a surrogate model based on the radial basis neural network. The optimal design was found to increase the stall margin by 51.36% compared to the case without the recirculation channel with only 0.55% and 0.28% reductions in the peak adiabatic efficiency and maximum pressure ratio, respectively.