Songbird does not allow you to interface with it remotely by default. To use it with Tesla, you must first install the 'MPRIS' add-on:
You should now be able to connect to Songbird from Tesla, and your setting should be remembered from now on.
NOTE: If you downloaded Songbird manually, you may need to run the following command in a terminal to ensure Tesla can find it:
sudo ln -s /path/to/songbird/songbird /usr/local/bin/