Leia had a bit of time to prepare herself for this--at least as much as she possibly could. It had never crossed her mind that this would be a possibility.

Even if she'd thought she was ready to deal with this, it's one thing knowing that an encounter with the time-displaced man that was her biological father is going to happen, and it's quite another for it to actually happen. She's calling on all her not-inconsiderable diplomatic training to keep a calm face, but her mind is racing either way.

"Thank you for your assistance, General Skywalker." When in doubt, fall back upon respect and formality.