The hysteresis properties in bistable polarization switching (PS) of vertical-cavity surface-emitting lasers (VCSELs) induced by variable-polarization optical feedback (VPOF) are investigated numerically. We mainly concentrate on the influence of sweep rate of the polarizer angle on the bistable PS for the cases with different feedback strengths and feedback delays. The output in the time domain and the representation on the Poincare sphere plot are further presented to describe the two PS processes. The results show that the size of the hysteresis cycle of the PS follows a power-law relationship versus the sweep rate of the polarizer angle, and the feedback strength and feedback delay can modify the hysteresis properties significantly. A larger feedback strength leads to a narrower hysteresis loop, while a larger feedback delay gives rise to a wider hysteresis loop. Therefore the VPOF provides a new method for obtaining the controllable bistable PS in VCSELs, which is potentially interesting for applications that require polarization-bistable VCSELs.