"They mirrored each other in surprising ways since the bonding, emotionally and otherwise. Why, her courses had shifted by more than a week to match the other woman's!"

It's plain spoken here that her body adjusted by more than a week to match Birgette's, but it doesn't rule out the idea that it was the only change. Birgette's may have well shifted the other way in a mirrored fashion, as could be inferred by the first sentence. In reality, I don't think it would really matter whether or not Birgette's shifted at all. Birgette's situation is one that has never (to our knowledge) occurred before. Jordan said that Moghedian short-circuited the pattern by forcing Birgette from Tel'Aran'Rhiod into reality, so all thoughts on what "should" be can be thrown right out the window.

I also find it as plausible that since Birgette is described as a woman older than Elayne, when the pattern forced her into existence, she came into existence as an older woman, as if she had lived her entire life up to that point. Given that, I would think that a younger woman would be more influenced by an older woman when their menstrual cycles align themselves. (Also note that this isn't a unique phenomenon. In fact, this has been proven to happen in our reality more than just a handful. It's almost a common occurrence for two women living in close proximity - i.e., mother and daughter, two sisters, or roommates - to have their menses off themselves by up to two weeks in either direction to match the other's.