Question: How can I take a screenshot of my PC's BIOS?

Answer: 
Take a camera, point it at the screen and take a picture.

Unless you have some kind of very fancy KVM switch that works over network (no, the cheap home user ones don't do that). Then you can do a direct screen capture on the receiving end, I think. Requires another computer, though.

Yet another option would involve a graphics card with TV out, a video capture card and another computer too. And some hope that video out works in text mode out of the box. I think you can guess where that goes.

Seriously, take a camera. It's by far the easiest and quickest way of getting a screen grab of something that happens way before you control the computer.
You can use an IP KVM switch with 'BIOS level access' (not exactly cheap though) and access the BIOS 'remotely' from another machine and take 'proper' screenshots there.

![enter image description here](https://i.stack.imgur.com/AfSLf.jpg)