Is there any advantage to using a weather resistant GFCI in a bathroom?
Probably no reason to use a WR outlet. The "WR" rating may not mean what you think it means. The primary difference between a WR outlet and a regular one is the WR one uses a special kind of plastic that does not get as brittle when cold and has better UV protection so it does not get damaged by direct sunlight. It does not provide any additional water resistance. If the outlet is going to be subject to direct water spray (either indoors or outdoors) it should be protected by a weatherproof outlet cover.

(It's possible a Tamper Resistant outlet would provide a small amount of protection against water since there are shutters that cover the slots, but that's certainly not what it's designed for. You may or may not want to install TR outlets, depending on whether it's required by code and/or you have kids.)