The Handbook is not as clear as it used to be, but the records of bishops of YSA wards should be kept in their geographic ward and the YSA unit creates an out-of-unit record for them.
See General Handbook 33.6.5 and 33.6.6.
More info at
Help Center: Out-of-Unit Members and Callings
So, what should happen is the bishop's records go back to his home ward and the YSA stake adds an out-of-unit record for the bishop and assigns his calling. (I don't think the ward can record the calling of a bishop.) Of course that will temporarily release the bishop and generally make a mess of things in the short term. But that's the only way to be ministered to by the geographic ward since out-of-unit members do not show in ministering. (So the geographic ward can't be the one with the Out-of-Unit record.)
I don't think there's any official provision for the bishop's wife. But the YSA ward can add her as a out-of-unit member. But may not get full rights until assigned a calling.
I'm sure someone will correct/update me if I'm wrong.
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