If you have everything gutted, now is the time to bring it all up to new code revisions (that are actually pretty old).

Bathrooms are required to have 20 amps for the required GFCI protected receptacle.

Why would you run 12/2 on a 15 amp circuit?

15 amps is on the low side for outdoor receptacles.

that is very helpful, thank you

If it is an outdoor receptacle it can't be on the same circuit as the bathroom receptacle. Bathroom is required to be dedicated to bathroom only.

I think your question is, "I want to add an outdoor receptacle by connecting to my bathroom circuit and I have this piece of 12/2 cable sitting around. Can I use that instead of running out to the home center to buy 14/2?"

The short answer is, yes, you can use a heavier gauge wire.

As others have pointed out, current code requires bathrooms to be served by a dedicated 20 amp circuit. So it might not be bad idea why you have the walls open to run a new 20 amp circuit for the bathroom.

If you use high draw outdoor electric tools (leaf blower, etc.) you might want to make that receptacle on a 20 amp circuit as well (although not the same circuit as the bathroom!). If all you plug in is Christmas lights (and your last name isn't Griswold) then 15 amps is fine.