Thanks for the response. Glad to know that I am not the only one having this problem. Having said that...I believe, for several reasons, that this is actually a feature / glitch in iphone 5.
To the best of my knowledge this problem does not exist on previous versions of iphone. Secondly, once my iphone is connected to bluetooth, it does not even allow me to set any of the ringtones or alert tones associated with texts, voicemails or notifications. Try this with your phone...once it is connnected to your car's bluetooth, go to Settings - Sounds - Text Tone (or New Voicemail). Select any of the Alert Tones or Ringtones. If you have set your phone to vibrate for Text, it will vibrate, but you will not hear the tone. The same Alert Tones or Ringtones will be audible if you had selected Ringtone (phone ringer) instead of Text Tone or New voicemail in the previous menu. This tells me that the problem has nothing to do with the size of SMS tones or the bluetooth being in the idle mode.
Furthermore, I have the Tunein Radio app on my phone. The second that my phone is connected to bluetooth, I loose sound from the radio app. Not only does the radio app not play through my car's speakers, it also stops playing through the phone's speaker.
So all in all I believe this is an Apple issue that they need to resolve. Finally, I understand that we should not text and drive. But Apple should not be in the business of restricting what an individual can or cannot do. Playing the sound simply serves to inform the owner of a new text or voicemail. It is up to the driver if they wish to respond to it.