Mike, I should clarify that in this scenario, by bluetooth I mean stereo systems that make stereo music available as a service on bluetooth, not just voice.
For example, my friends car (Mercedes) has bluetooth built-in to the factory system. It pairs automatically whenever he turns on the ignition. But that stereo is NOT capable of streaming music through bluetooth, just voice. Our Droids look at services available after pairing with bluetooth and if stereo music streaming isn't one of the services, then it will not automatically start playing the music player.
I have a separate bluetooth adaptor installed in my car and hooked up to my factory stereo system where it is capable of streaming music (Alpine, Parrot, etc). In this case, my music automatically starts playing everytime I turn on the ignition. I believe the OP also has a system with streaming music capabilities.
Also, try plugging in a set of stereo headphones. You should also hear music playing instantly!
Not sure if rooting makes any difference. I'm not rooted (FRG01B).