7. SSH Tunneling
If direct connections are not allowed there is another way - secure SSH connection. Actually SSH is a kind of tunnel between two computers - your computer and your server. Other connections can be established via SSH tunnel.You can use SSH for MySQL as well as for FTP connections. See "Preferences" window, "SSH" page. The only info you need is SSH user name, password and remote port number - basically the same as for typical MySQL connection.
Note: SSH settings do not override MySQL settings. To connect to your database using SSH you must specify all the required MySQL parameters as well as SSH. If neither direct MySQL nor SSH connections are possible, PHP MySQL Bridge connection can be used.