This is different than revealing a moat infinitely. With the moat example, at each point you make the decision "do i want to reveal moat?", and as soon as you stop, the game continues. The game never really locks because you could just choose no at any point to continue.
With this case, once you play your BoM, the game, not the player, generates an infinite sequence of events playing BoM. Neither player can choose to stop it. If you did this in dominion online, if it is implemented correctly, the game should immediately crash for reaching a truly infinite loop.
MtG explicitly distinguishes these cases in the rules. In the first case, if either player can make a decision to break the loop, they must do so. In the second case, MtG declares the game a draw.