If it's just a matter of using your existing skills without having to learn something new, then you can hack something together between an Arduino and the Bela Digital I/O pins. You can invent your own protocol to command the Arduino on the Bela Digital I/O pins, clocked at audio processing rates.
I2C and Serial are simple because you just send the text you want to display and simple control codes out the serial port or I2C bus.
giuliomoro pointed to a thread to help get going with I2C if you decide you want to try that route.
If you think you want to try the Serial route, here's one example for Bela (maybe you already perused it):
https://github.com/transmogrifox/Bela_Misc/tree/master/audio_level_meter
https://github.com/transmogrifox/Adafruit_USB_Backpack_Plus
The code assumes my hack of USB BackpackPlus with the audio level meter function and a 20x4 LCD.
If you don't care about the audio level meter then you might glean more useful stuff focusing your attention here:
https://github.com/transmogrifox/Bela_Misc/blob/master/audio_level_meter/usb_backpack.cpp
In my application, the USB stuff is handled behind the scenes by the driver Linux uses for USB-serial devices. As far as my program is concerned I'm interfacing to a serial UART, and this code could just as easily use a BeagleBone UART on TX/RX pins on the header simply by changing the file descriptor to the device name for a BBB serial port.