Bluetooth has a variety of operating modes. One of the more common is SPP, which basically makes it look like a serial port. Audio devices usually use two or three of other possible modes. You need to make sure your bluetooth device on the arduino side supports this. You then need to support pairing. The device on the arduino side likely needs to initiate this; including supplying the pairing code.
Once you have then pairing and talking, I imagine you'll then have access to an audio stream of some type. What you'll do with that and if you'll have enough processing power to actually do something with it on the arduino are different questions. I suspect you'll need some sort of audio co-processor. Which is likely why PaulS said its not normally Arduino's strong suit.