The inversion states of a saturated three-level traveling-wave quantum paramagnetic amplifier have been investigated under conditions of bistable resonator pumping. The equations of motion for the vectorial order parameter have been obtained using adiabatic elimination of fast variables. These equations are a generalization of the scalar two-level Drummond model for the case of a three-level quantum active system. Isolated branches of the constant of inversion have been found from stationary solutions of equations for the vectorial order parameter. A analysis of bifurcations in the saturated quantum amplifier with bistable pumping has been represented with full details.