In Chapter 55, when Bingley comes to visit Longbourn again, JA writes, "She then sat still five minutes longer; but, unable to waste such a precious occasion, she suddenly got up, and saying to Kitty, "Come here, my love, I want to speak to you," took her out of the room. Jane instantly gave a look at Elizabeth, which spoke her distress at such premeditation, and her intreaty that she would not give in to it."
Was this improper? Why was Jane so frightened to be alone with Bingley? Wouldn't she wish to give him an opportunity to propose? Surely, it's embarassing to have a mother behave in such an obvious manner, but if she's going to do it anyway, why persist in keeping Lizzy in the room? Why not take avantage of the situation?