Nyquist-Shannon simply says that you need 2x the sample rate of the highest frequency to perfectly recreate something. So, to recreate a 20 kHz wave that was sampled at 16 bits, you'd need 40 kHz sample rate. Bump that up to 22.05 kHz (for anti-aliasing) and you get CD audio.

The bit depth, OTOH, is your signal-noise ratio (noise floor) when sampling/quantizing said audio. It's unrelated to Nyquist-Shannon. More bits gives you less noise when reproducing it. For CD audio, 16 bits was chosen to give an acceptable SNR of 96 dB.

Monty Montgomery (of xipf.org) has a nice YouTube video related to this: https://www.youtube.com/watch?v=cIQ9IXSUzuM