It seems to me there are a few variants from an engine perspective.
- 1 Engine plays on two boards and has full control.
- An instance of an engine plays on one board and another instance of the same engine plays on the other board.
- An instance of an engine plays on one board and another agent (engine or human) plays on the other board.
Compared to crazyhouse, bughouse has a number of additional elements. Notably, a player may choose to not make a move in order to prevent the opponent from giving their partner material. In engine bughouse, ideally there is some command to wait until something has occured, so if all 4 players call the wait function, the clocks could get artificially adjusted to save time. I am not sure what kind of time controls are ideal for bughouse nor the exact ruleset that would be interesting for engine play. However, I do feel like bughouse should have a much higher skill ceiling than crazyhouse or regular chess.