If so what's the use of the CP2102?
The main difference between a Nano and a Pro Mini is that the first has the CP2102 (or CH340) and USB socket.
A ready-made Bluetooth microphone would do.
Or maybe a Teensy, it can do 44 kHz audio, at least mono.
Don't you need compression for audio over bluetooth? The Arduino can't do much (not enough processing power) of that, a teensy is definitely better, a purpose-built IC is certainly best.