You're in an emulator - you don't have to switch to protected mode within the emulation, you can instead exit the VM and do the work outside the emulation. The caller within the emulation won't notice unless it's trying to single-step the BIOS code (and why would they do that?).

Edit: unless the code within the emulator is trying to run the BIOS within an emulator of its own. Turtles all the way down...