Arduino  BBB UART issues using bi-directional level converter (5v to 3.3v)
Strangely it seems as though the Arduino is outputting voltage over both RX and TX, while the BBB is only outputting voltage on the TX line. 

My guess is that the bi-directional LLC isn't able detect which direction communication is supposed to happen, and so the BBB isn't able to transmit to the Arduino.

This Sparkfun LLC is the same as the one I'm using on the BBB -> Arduino channel, but the Arduino -> BBB side just uses a voltage divider. I rigged up this setup, and it seems to be working now.