We report on the impact of realistic gain and loss models on the bistable operation of nonlinear parity-time (PT) Bragg gratings. In our model we include both dispersive and saturable gain and show that levels of gain/loss saturation can have a significant impact on the bistable operation of a nonlinear PT Bragg grating based on GaAs material. The hysteresis of the nonlinear PT Bragg grating is analyzed for different levels of gain and loss and different saturation levels. We show that high saturation levels can improve the nonlinear operation by reducing the intensity at which the bistability occurs. However, when the saturation intensity is low, saturation inhibits the PT characteristics of the grating.