It works well. Good news the code is freely available on Github. But first a photo:
The LCD I use is LinkSprite 16 X 2 LCD Keypad Shield for Arduino. It's available at SparkFun (here).
The 4 bit mode used less GPIO on the BeagleBone Black than the 8 bit mode.
I am currently working with an OLED screen. I'll keep you in touch.