I just picked up my new '10 3 today with Tech and spent a good chunk of the afternoon messing with Bluetooth. In the owners manual there is a extensive section on how to do this. I think it takes default codes of 0000 or 1234 on your other device (phone etc.). The salesman paired my phone for me using the voice menu, he did it quickly and I don't recall him doing anything on the phone at all.
I think the way it works is that if your other device has a pairing code of 0000 or 1234 the car will find it automatically when you go into pairing mode. If the device has some other code, when you are in the pairing menu on the car there is a way to enter a different code using the radio station preset buttons to change the pair code on the car to match the device you're trying to pair. Hope this helps.
I was trying to pair a BT Ipod adapter with my Ipod to the car. I could not get it to pair, the BT adapter was a cheap one and I have a feeling that is the problem not the car.
I think according to the owners manual there is also a dedicated website for BT issues, I think it was www.mazdausa.com/bluetooth