Make sure she knows that you have multiple other reasons for being there
that takes the pressure off the situation. Keep your first date relatively simple and give both of you a chance to talk in person. No movies, plays, etc. I always kept my first dates post-divorce fairly short and then if it went well, had a longer date later. Think of your first half dozen dates as practice. You'll need them to work the bugs out anyways. If you marry the first girl you go out with, you are probably doing it wrong.
All that said, do whatever works for you. Good luck. I met my wife online and went on our first date on a business trip that I was able to arrange to be in her neck of the woods. She said the business trip helped her feel much more at ease since she wasn't the main focus of my trip. We've been married for 3 years and have a 2 yo daughter. Life is great.