A supersonic gas compressor with bleed gas collectors, and a method of starting the compressor. The compressor includes aerodynamic duct(s) situated for rotary movement in a casing. The aerodynamic duct(s) generate a plurality of oblique shock waves for efficiently compressing a gas at supersonic conditions. A convergent inlet is provided adjacent to a bleed gas collector, and during startup of the compressor, bypass gas is removed from the convergent inlet via the bleed gas collector, to enable supersonic shock stabilization. Once the oblique shocks are stabilized at a selected inlet relative Mach number and pressure ratio, the bleed of bypass gas from the convergent inlet via the bypass gas collectors is effectively eliminated.