Not sure how much warming up a position player does before going in to pitch in a blowout, but I don't think they usually go to the bullpen. Most stadiums have indoor batting cages that players can go to before pinch hitting so someone could probably throw in there to warm up.
I'm sure a rule about it could be written if there isn't already one that would allow Ohtani to go warm up in the bullpen even if he was already the DH. I still think the bigger problem is getting him time to warm up without his spot in the order coming up to bat.
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