There are all kinds of BT interface devices you can buy off ebay that will do what you want ...and they're not that expensive. You'll need to remove and tap into your radio. There are tutorials out there.
My H3 has the GM factory radio with DVD navigation, and Monsoon system too. The guy who owned my H3 (before me) installed such a device, only mine has an 1/8" jack (I wish it was bt but I have to plug mine in). It's hooked into the XM portion of the radio. There's a small control board hidden behind the center panel, which, when it detects a signal from my phone, bypasses the XM signal and plays my phone over the XM portion of the radio. He chose XM because it was the feature he didn't use much. Or maybe that was the type of device he purchased. He was telling me but his english was so-so. Anyway, it works great. When my phone isn't playing music, XM works as it normally would. If you go that route, you're gaining bt, but not losing any functionality.
If you're happy with your OEM radio, or want to keep it all stock, then this is a nifty and cheaper solution than a new radio. Plus you get to keep all the OEM interfaces. On nice reason to choose a new radio would be for a back up cam. I'll see if I can find a link.
Note: See links in post below.