Beatrice doesn't come across well in this book at all. From everything the narrator tells us, she sounds like a nervous and entitled woman who expects everything in life to go her way. She also believes herself to be a "high class" person, because of her money and education.
As the book tells us, "A brilliant education she had—her youth passed in renaissance glory; she was versed in the latest gossip of the Older Roman Families" (1.1.2). Some people would take a good education and use it to help the human race, or at least to stave off boredom. But Beatrice is more interested in using her education for superficial purposes… like convincing everyone of how impressive she is.
Beatrice is a heavy drinker and proud of it. Throughout this book, she uses her ill health as a symbol of how refined and delicate she is. But when it comes to drinking, she sees her own survival as a mark of toughness. As she tells Amory:
"The doctors told me […] that if any man alive had done the consistent drinking that I have, he would have been physically shattered, my dear, and in his grave—long in his grave." (1.1.156)
That's a weird thing to brag about, in our humble opinion.
Ultimately, Beatrice sees herself as a tortured soul—someone too deep and sensitive to be appreciated by the rest of the world. The contradiction here comes from the fact that rather than being deep, Beatrice is actually obsessed with the surfaces of things, like people's appearances.
Nonetheless, she insists to her son, "I am not understood, Amory. I know that can't express it to you, Amory, but—I am not understood" (1.1.164). It's clear that Beatrice has a big effect on the formation of her son's personality. But as the narrator consistently reminds us, her influence isn't a good one.