Bluetooth or wireless headset mic for recording voice (for online training)

so my wife needs to be able to record her voice for some web training while moving around a small room.

I can see two approaches:

1. traditional professional - a headset mic, a wireless send/receiver, a mic pre-amp into recording device (analog/digital)
2. enthusiast home user - a bluetooth headset w/mic - either with USB receiver OR just direct to recording device (inbuilt bluetooth on laptop)

Can anyone comment on if the second approach can yield good results for voice recording?

Ideally it's a low profile headset mic, so not a big gaming style headset.

thanks!