I'm not 100% sure on this but I think you can add the BT module from GM to your factory system. I was looking at doing that our 2011 Acadia but other things came up so it got put on hold. It is a nice feature. I installed an aftermarket Alpine in my truck and it's so nice to listen to music from my phone and not have to plug it in.
What Alpine head unit do you have? I have an Alpine in mine, but it's an older model from 2007 or 2008. I can "add" Bluetooth if I buy an external module from Alpine, but for what that module costs, I can actually buy a newer head unit. I've been considering converting my dash to the 2003-2006 dash so that I can install a double din style larger head unit. Other than NO Bluetooth, I actually like the unit I have. It has pretty much every other feature I want or need, all the aux inputs and everything, I have my DVD player on one Aux input, then it has an iPod input/interface, and it also has a USB port that I can plug in a thumb drive full of music. My only real benefit of getting a double din would be to have a DVD player built in so I wouldn't need a separate DVD player, and to have Bluetooth built in.