Any normal SMPS plugpack is already isolated from mains, or you'd get a shock if you touched the output. Some grounded plugpacks connect the output ground to the mains ground, which is perfectly safe. Non-grounded plugpacks will generally contain a Y capacitor, which will present a small mains leakage current to the secondary side - but this applies regardless; if it's safe to touch in the living room, it'll be safe to touch in the bathroom.
So yes, a 12V PSU will be safe for a bathroom. If you try really hard, you can electrocute yourself with it, but it's no more dangerous than a couple 9V batteries in that regard.
LED lighting fixture PSUs may or may not be isolated. Do not count on them being isolated, or their isolation being sufficient for safety purposes.