Short set of notes.
The most reliable way I’ve found to connect to a remote device is to open a connection immediately after connecting the USB cable to the PC.
At this time, I haven’t figured out a clean way to disconnect and reconnect without physically unplugging. Closing the screen session (ESC->CTRL+A->SHIFT+D->SHIFT+D) makes follow-up connections via the same line unreliable.
EDIT: This should work: http://askubuntu.com/a/661/364657
Connections require the Black GND (Ground), White TX (Transmit), Green RX (Receieve) pins connected. Connecting the Red VCC (Power) pin is STRONGLY discouraged.
Reference: http://linux-sunxi.org/UART http://linux-sunxi.org/LeMaker_Banana_Pi#Adding_a_serial_port
Other methods: https://www.chromium.org/chromium-os/how-tos-and-troubleshooting/debugging-tips/target-serial-access
And if you’re feeling silly, data can be send directly to the connected TTY like so.
Extra
I’m running Armbian (Ubuntu 14.04) on my Banana.