I believe that on the C6 A6s the only way to get Bluetooth (factory fit) was to have either the Low or High Telephone option. Both gave you fittings in the driver's arm rest. Therefore if you have no contact panel showing in the arm rest then it is very unlikely you have Bluetooth fitted. There are some aftermarket options available that will integrate Bluetooth with the MMI system or you can go for a standalone option such as one from Parrott.
There are a couple of Mobile Phone connectivity options available on the C6 A6......
The GSM factory fit comes with the front arm rest connections and Bluetooth. However, there is also a bluetooth factory fit which was only available with MMI High and does not have any front armrest connections unless the optional wired privacy handset was spec'ed with the car.
(Data taken from October '07 A6 Sales Brochure....)