Princess Betsy Tverskoy is the queen of elite, morally liberal Petersburg society. In her set, marriage is an old-fashioned idea that nobody respects (but that everybody does, for form's sake). In her world, the goal is to live high on the hog, to gamble and to have fun, without worrying too much about things like religion and morality.
Princess Betsy is the total opposite of that other great Petersburg social figure, Countess Lydia. Where Princess Betsy is young and lovely, Countess Lydia is and older woman. Where Princess Betsy dismisses morality, Countess Lydia is obsessed with moral judgment. However, these two women are similar in that they're both the heads of important Petersburg social crowds, and they're both hypocritical. In fact, Betsy acknowledges that, when she loses her good looks, she'll probably take up religion and good works as a hobby as well: "When I'm old and ugly, I'll become like [Countess Lydia]" (2.4.4). Yowch, that's cynical.
For now, though, Princess Betsy is lovely, cold, and vicious. Even though she's in the midst of her own affair with a man named Tushkevich, she abandons Anna, telling her "she didn't want to know [Anna] as long as [her] situation [with Vronsky] was irregular" (6.23.20).
Princess Betsy's hypocrisy—that she's willing to put aside her own marriage when it suits her, but Anna's love for Vronsky somehow goes too far—demonstrates once again the weakness and fakeness Tolstoy saw at the heart of Russian urban society. In fact, Karenin says as much, seeing in Princess Betsy "an embodiment of that crude force which was to guide his life in the eyes of the world and which prevented him from giving himself to his feeling of love and forgiveness" (4.19.48). Princess Betsy represents that "crude force" of society that ruins Karenin's religious epiphany and that throws Anna into the profound isolation that drives her mad by the end of the novel.