Engadget
How to add Bluetooth to a TV that doesn't have it

If a TV lacks built-in Bluetooth, you can add it with a streaming device such as Apple TV, Roku or Fire TV Stick, which provides Bluetooth for headphones or keyboards but only when that input is selected. Alternatively, a dedicated Bluetooth transmitter plugged into the TV’s optical, 3.5 mm, or RCA audio output (powered via USB) works with any source; models around $25 with aptX Low Latency reduce audio lag.