One of the movie versions has a scene with Elizabeth receiving a note from Mary, but it is not so clear in the book. It could be Anne receiving the note from Mary and discussing the situation over with E.

''Something occurred, however, to give her a different duty. Mary, often a little unwell, and always thinking a great deal of her own complaints, and always in the habit of claiming Anne when any thing was the matter, was indisposed; and foreseeing that she should not have a day's health all the autumn, entreated, or rather required her, for it was hardly entreaty, to come to Uppercross Cottage, and bear her company as long as she should want her, instead of going to Bath.

"I cannot possibly do without Anne," was Mary's reasoning; and Elizabeth's reply was, "Then I am sure Anne had better stay, for nobody will want her in Bath."