Caroline Kennedy arrived at the Monkey Bar with ashes on her forehead yesterday. Coming from St. Patrick’s Cathedral after Ash Wednesday Mass, she confessed she had to go to two churches in the morning because, “I missed the first service . . . I’m going to give up cookies for Lent,” she told us at the Public Prep Network Namesake Luncheon. “And I’m trying to be a better person.” Would she resist meat? “Depends on what they’re serving,” she quipped. Later, we asked Kennedy about her passion for education reform, and whether she’s considered running for office to change the system. “I don’t know,” she said, declining further questions. Others at the lunch for Public Prep, a nonprofit that runs girls’ charter schools and will soon open one for boys, included former Schools Chancellor Joel Klein, who introduced Kennedy, Joan Ganz Cooney, Liz Abzug, Celerie Kemble and Boykin Curry, Laura Weil and Holly Peterson.