I think I should add that the ceiling in the bathroom is a standard height. Although ceilings in the rest of the house are higher, they are not in the bathroom or kitchen, which I suspect may have been added on to the house at some point in the distant past. And, there is no window in the bathroom, as we had to give up the one that was there during a garage addition.

Your other option is to have it cover 1/3 of the wall. If your ceilings are 8', the standard height sold should fit the bill. There is less chance it would interfere with a mirror that way.

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Wainscoting panels is traditionally done at the chair rail height, to protect walls from the backs of chairs rubbing against them. A partial judge’s panel look is typically done 1/2 to 2/3 up, depending on the ceiling height, in order to provide a picture ledge to lean fine art on. Since a bathroom doesn’t have chairs, and very little fine art, Id suggest skipping any wood coverngs entirely. Maybe do a traditional wallpaper.

I would do tile instead of bead board.