I can't comment on city 2012 model. However, I own a brio which comes with stock audio, andit does not have bluetooth connectivity. However, it has an aux input, which I belive is also there in city 2012. What I did is simple. I bought a bluetooth nokia headset with a2dp profile. The headset has a 3mm headphone input. I paired my phone and attached a male to male aux cable connecting the bt headset with the aux input. Voila....job done.
Whenever a call comes, I just simply flick it to aux source for the conversation. Moreover, now I can listen to songs from my phone wirelessly, even connected my ipad and and listened peacefully to my itunes playlist.
Try this, your requirement might be achieved.