How Good Is Audio Quality When Using An Amp's Bluetooth Connection

Let your ears be the judge. I don't even use bluetooth in my car but hardwire the phone into the car's system.

I've asked the same question and found this to be a pretty helpful explanation of the issues.
https://pitchfork.com/thepitch/1305-does-bluetooth-really-sound-worse/

I have a bluetooth adapter for both headphones and my main system.  I find the sound to be noticeably inferior in both cases.  I would compare it to the difference between redbook CD and mp3.  It is not unlistenable, but it is easy to tell the difference.

Bluetooth is generally inferior to wired or WiFi connection. If both sides support aptX, quality takes a step up; if they support LDAC, another small step. Still, for my main system, I'd prefer an uncompressed connection.

At AXPONA, Audioengine was demonstrating their speakers with Bluetooth. In my opinion, they did themselves a great disservice, as the sound was pretty flat and gray.