The SoundDock III has an audio input connection in the back, allowing you to feed in an audio signal. Technically speaking, this port could be used to connect an adapter such as the SoundTouch Wireless Link Adapter, which has WiFi and Bluetooth compatibility.
This means you could connect to the adapter via Bluetooth, to stream music from your Bluetooth device. Alternatively, you can use the SoundTouch app to connect the adapter and stream audio via WiFi. You can learn more about this product HERE.
I also open this to the Community to input any experiences or share their ways of bringing Bluetooth compatibility with this speaker.