That means that the water intake could have been from trying to breathe through her nose, rather than her mouth...

That's right! The bathtub was only slowly draining because of the paper that had been from her mouth was clogging it, which means that she couldn't have been drowned in the bathtub. If you're using a sink to drown your victim, then the one place that will be dry is probably going to be where you place your hand. [ She reaches behind her to touch the back of her head as if to make a point. ]

She was fully clothed and had make-up on, which means she wasn't planning on taking a bath in the first place.