We present experimental and theoretical results of bistable polarization switching in a single transverse mode 1550 nm vertical-cavity surface-emitting laser (VCSEL) subject to parallel optical injection. We focus our analysis on the bistability induced by power variation of the master laser found on the recently observed state of simultaneous injection locking of the parallel polarization mode and excitation of the orthogonal polarization mode, IL+PS. Experimental stability maps identifying, in the injected power-frequency detuning plane, where this state is observed, and corresponding bistable regions are reported for several bias currents. We find bistability between the IL+PS state and the single polarization mode injection locked solution. We also find bistability between the IL+PS and different periodic dynamics in the parallel polarization mode. The width of the hysteresis cycle increases when increasing the bias current or when increasing the wavelength of the optical injection beyond the solitary VCSEL wavelength. We theoretically confirm these types of bistability by numerically simulating the spin-flip model and by performing a linear stability analysis for the different stable states. Excellent agreement is found between experimental and theoretical results.