If you don't want to power it while the car is off, what I would do is hook it up to the battery as NorCalDC4 suggested, but I would either put a relay switch that gets it's activation from the atteana power line, or just put in a toggle switch somewhere. So, basically, the FM modulator will not receive power unless the atteana is up, or you have the toggle switch activated, depending on which way you choose to go.

And I would just cut the bullet connector off and use the connection you would find most convenient for your setup...