The author of “Once Upon a Secret,” Mimi Alford, had an affair with President John F. Kennedy before she was old enough to vote. Having kept this story under wraps for almost 50 years, Ms. Alford now sets off a firestorm of gossip about its sordid details. If there is one question that Ms. Alford’s story poses, it is this: How did she end up in bed with the president on her fourth day at work? This may be the hardest part of her adventure to imagine, but it’s what she explains best in the half of this book that reconstructs a 19-year-old’s thinking. She was invited to swim at lunchtime in the White House pool. She couldn’t say no. The president arrived unannounced, asking, “Mind if I join you?” She couldn’t say no to that, either.