Your sentence "The protocol just needs to send each bit twice (or any multiple of two) at 20KHz." nearly makes no sense. You should learn about modulation, sampling, aliasing, and so over.
If you want to stay ultrasonic you will need to use a narrow bandwidth around 20k, otherwise people with a good hearing and children will be able to hear it. I don't think you'll be able to receive anything useful by using a cheap PC microphone at 10k in those conditions, especially if you use it in the way it is intended to be used (the hardware will filter out high freq to prevent aliasing)... Maybe there is a convoluted way to receive a specially crafted transmission by sampling in a subharmonic when a special antialias filter (or no filter at all in otherwise quiet environment) is used.
I don't see much point in trying to use such a channel to transmit bios malware related stuff anyway. The original badBios article seems to be just a joke.