A possible solution is to use a Raspberry Pi for display, and use the PI to connect to the BBB.
If the main goal is to avoid having a separate computer then this comes close since you can locate the PI into the same enclosure with BBB + Bela without taking up a great amount of extra space.
I sometimes use the Bela IDE through a Raspberry PI w/ HDMI display, keyboard, mouse, + Desktop Environment. It works fine.
I don't know if this idea helps, but there it is.