I looked, but could not find but a small reference to this, with no links.
The easiest solution, by far, to add Bluetooth to a 2011, or earlier MB is to use CoolStream's CarPro Bluetooth adapter.
It attaches to the 30 pin Aux cord in your glove box and you stream your iPhone and even Android phone to it.
You're still able to use your steering wheel controls (limited display w/Android) and it works like a charm!
I wish that I had seen this earlier.
Here are a couple of links to help you...


https://coolstreamrocks.com/

 

This assumes you have the 30-pin iPod interface. If you don't have that, since it's out of production, it's becoming more difficult to find. But if you do, this is a good product. I have on in the SL. I do wish it had more "smarts" and would translate Android playlist and song title info. For Apple users, it shows everything just as if an Ipod were hardwired. One problem I have with it is that if you also have a hands-free calling interface (like I had on the SL's NTG 2.5 COMAND), it does not play well with that. It will cause your call audio to frequently drop out. I have talked to CoolStream about this and they gave me all sorts of suggestions, but nothing helps. I think it's a bug in their device.

 

I would agree that the CoolStream is a viable Bluetooth solution for music (taking into consideration the caveats mentioned by Rudeney above), but it doesn't do hands free calling. To me, it's sort of like half of a solution.

The LA Power/ Mr. 12 Volt product is the only reasonably-priced solution I found that has both music streaming and handsfree calling, and which (I believe) allows you to use steering wheel controls for both. I bought mine many months ago, but have been too lazy to install it. It doesn't look like it's available at Amazon any longer, but I think you might be able to find it on ebay.

Amazon link:

 

I think the Coolstream can output call audio, so using the mic on the phone, you would get hands-free, though you don't have any car controls over the answer or dialing functions.