You could have Person A (the revealer) subtly manipulate the conversation so that it looks like Person B brings the subject up. Not knowing your big secret, I can't suggest specifics, but something like this:
They sit around the campfire drinking. Person A looks up at the trees around them and shivers, saying, "The woods have always seemed so threatening. Bears, wolves..."
Person B then says, "Yeah, but the outlaws are the worst."
Person A jumps up. "How did you know my parents were killed by outlaws?"
Or...
Person A: "The city! It's fabulous. I remember a church procession there, where the archbishop's robes were embroidered in real silver! Can you imagine anything more impressive?"
Person B: "That's nothing--have you never seen the royal family? When the Prince came home from the wars, even his saddle blanket was embroidered with jewels."
Person A: "You're mocking me, aren't you? You somehow found out I am the Prince!"