I too think that maybe Anne and Charlotte might have struck up a friendship, if only because of the lack of other companions. Anne is isolated at Rosings with her mother and Mrs. Jenkinson, and probably has never had a really close female friend. The only other female relative we know of is Georgiana, and she lives at a distance and is much younger. The fact that Anne drives by the parsonage almost every day to speak to Charlotte -- even though she rarely deigns to enter the house -- shows that she enjoys Charlotte's company, or at the very least, that she is glad to have an excuse to visit someone and get away from her mother for a few minutes.