I think the easiest way to do this is practically – you need to build a bathroom that looks like the mirror of your bathroom. Basically, you need two sinks, two faucets, two sets of lights, etc. All designed to make it look like you’re looking in a mirror but actually, there’s no glass.
Then, you shoot over the shoulder of a stand-in, looking at yourself acting the part of the “mirror person.” Creative editing would help sell the effect. Not a lot of After Effects involved in this – it’s all practical.
I remember a similar scene from the movie “The Final Cut” starring Robin Williams. https://www.imdb.com/title/tt0364343/
At the very end, Robin Williams is looking in the mirror at himself (obviously a stand-in) and then the stand-in leaves the scene, but Robin Williams (as the reflection) stays behind, ruining the effect, but adding to the drama.
Regardless, this may give you an idea of how to frame and shoot your effect. I still think that this would be better done outside of After Effects with more emphasis on editing.
Good Luck,
Jacob