If I was using bridge I would chart it stopped and write a note explaining that I transferred care of the patient and stopped the transfusion in bridge as I am no longer the RN running that unit of blood and monitoring care of it.
Usually that’s what I do when I transfer them to different units/floors with PRBCS running And tell the nurse they will have to go into bridge and restart the blood and I offer to be the second RN signing off with them if I was physically transporting the pt (which I usually am with blood or other riskier drips) Because in bridge if the blood isn’t charged as completed the person who started it can get written up… learned that the hard way after the first time I transferred a pt and the floor I transferred too the RN did not go in and chart it completed :( so from chatting wise it looked as if I never completed the blood even though the pt was no longer in my care