In this case, the bit count is almost irrelevant. Here's why. To sample a 20KHz sound the sampler needs to run at 40KHz or higher. The bit count is more about the quality and depth of the sound, but not the possible frequency range.
You'll be out of running for most consumer camcorders and my have to get some ultrasonic recorders. If your school has an electronics division, take time to visit their gurus on such.
We want to do a project taping a bunch of environments with sounds just at or above the audible range... sort of a hearing test with psychology mixed in. Most mikes pick up just above the 20kHz range (which is at the high end for audio for most young kids), but a friend told me that most camcorders on the market use a Pulse Code Modulation of around 8bits ...a sampling rate that puts them down around 8kHz. I'm not sure I understand. But I'm seeing in camera specs an audio sampling rate of 16bits.... which still puts us below where we'd like to go with this. Is my friend wrong, or do I have to scrap this experiment?