Totally outside the scope of the novel, I know! but one way for shy people to 'come out of themselves' a little is to feel themselves to be of some use to others. Possibly, Kitty's need for some sensible companions would have been of great worth to Georgianna, making her feel helpful. An introverted person will never become an extrovert (although I have seen some excellent playacting done), but she could have begun to feel that less awkward and more engaged with someone around of whom she was not in awe.