That's what my Bluetooth headset can do, in a tiny package, far smaller than the Pro Mini alone.
If that's all you want why the extra parts like a display and CP2102? If you want USB get a Nano instead of a Pro Mini. Barely larger with the USB built in already, so likely smaller than what you're trying to cobble together with separate parts.
Also the ADC of the Arduino will never get good quality audio due to its low sampling frequency (maximum <10 kHz).