Firstly, try re-starting the BT module in the foam box under your seat. You should be able to lift it up (be careful, the velcro adhesive strips like to come off and stick to the carpet, use a torch and make sure this doesn't happen - if it does, just peel them off the carpet and re-affix to the foam container). Once you have the box up, you'll see obviously the connector you need to unplug, it has a mechanism that opens up, so don't just yank on it.
If this fails; get someone to scan your car using a VAGCOM cable to check for any errors that may explain the behavior.
At a pinch, I'd say the RCD unit is screwed if the reboot fails to do anything. I've installed tons of these in cars with factory bluetooth such as yours and never experienced such issues. Even when the BT module has a sad (and they do from time to time, the A2DP ceases working, bluetooth stops responding completely), they never exhibit this behavior. The fact it works from the MFD without incident = BT module is happy in the pants.
-Mythik
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