Thank you so much everyone for the lovely comments! Tonibun, we're going to bond them in an outbuilding attached to our house, it's used as a utility room but is only single brick so the temperature is very similar to outside. We'll thoroughly clean out Bea's hutch before they go back in there together and we're also going to move things around a bit/add a few new obstacles etc in the run so it is at least partially unfamiliar and new to Beatrice.
OK! Best of luck when the time comes.