I would run away from this as fast as possible! Believe me, I’m all for a challenge but that just sounds like too much work for a speaker. They have plenty of Bluetooth speakers for bathrooms.
I actually have an Echo 3rd Gen and Echo Sub in my master and it’s out of site, provides voice control for my automations and actually sounds pretty good.
However, the answer to your question is, you would need to have constant power at the box in the ceiling. It might already have it…
