Without the make and model numbers of your TV, Contour 2 and Bluetooth transmitter, I can only offer fundamentals.
You can connect a Bluetooth transmitter to 1 of 3 audio ports: - Composite Left/Right audio - 3.5 mm port - Optical TOSLINK
If you use the optical port, you will need a Digital-to-Analog Converter (DAC) to convert the digital signal into an analog signal. If your Bluetooth transmitter has a built-in DAC, you won't need another DAC. The Composite and 3.5 ports don't need to be converted because they're analog signals.