there's this project from a few years back that allegedly had AVB working on the BBB https://github.com/induarun9086/avbtest/wiki
We never tested it, but in principle if you follow the instructions there and it does work you should end up with a virtual ALSA interface, then you could use something like this(which currently only supports audio channels) to connect the non-realtime I/O from the network to Bela's audio, analog, digital I/Os.
Both projects linked above are unsupported afaik