Answer
When working with UwTerminalX, note that by default LineMode is enabled. With LineMode enabled, any data entered is not sent until the [Enter] key is pressed, as shown below:
To break the connection you must first disable LineMode, then when each character is entered it will be sent immediately over the bridge connection, without the need to press the [Enter] key. Now when four ^ are entered with a slight delay, the first three will be sent over the bridge connection, but the fourth one will break the connection, as shown below: