Broadcasting Bluetooth Audio from Arduino Mega2560

I have scoured the internet trying to find a shield that will allow me to broadcast audio FROM the arduino TO a pair of Bluetooth headphones, or even just a Bluetooth earpiece. I’ve seen dozens and dozens of serial Bluetooth modules, and even more Bluetooth receiver modules, but finding an Arduino compatible Bluetooth shield to broadcast audio seems to be a lost cause. Am I missing something here? I saw the one unit here (https://www.sparkfun.com/products/11777) but it seems to have a lot of issues with audio interference, so I was looking for any alternatives and have only been able to find mountains of serial transmitters and slave modules. I’m going to continue scouring, but if anyone has any experience with a good Bluetooth shield, please, let me know.

I somehow don't think you're going to be able to do this with an Arduino. I don't think you can sample the audio fast enough or with enough detail (the Arduino only has a 10-bit ADC). But hey, I could be wrong. That said, I think the first step is understanding how to encode the audio data for bluetooth. You'll have to research that. There's a protocol for that, and you'll have to match it perfectly or it won't work.

Found this that might help get you started:

http://www.crutchfield.com/S-nsyfDPrESA2/learn/abcs-bluetooth-in-the-car.html

https://www.bluetooth.org/docman/handlers/downloaddoc.ashx?doc_id=8236

You'll likely want to learn all about A2DP as that is the audio streaming protocol.

What if I already have a shield that processes the audio? I'm planning on putting a Bluetooth and a 3.5mm jack on the device for different audio preferences, but I'm also having trouble finding an audio shield that is compatible with the Mega 2560. If I find an audio shield for the Mega 2560, would it be feasible to route the pre-processed audio information through a Bluetooth transmitter? I've been reading up on the Bluetooth information a bit as well, but I'm still quite lost.