If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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Not sure how successful this might be, but would something like "Well, we've had a few interactions and I think we have a few things in common so I thought we should just hang out a bit and dget to know each other a bit better" Obviously you can change the wording a bit. Saying that you feel instead of think could have some implications but I'm not a lingustics-brain interpretation expert so I can't say I have much evidence to support it but that's just how I feel :) Anyway that hing is just a general guide-line and you could definitely change it a bit depending on the infinity plus one variations you have.
Also what is a relationship expert? Women? Guys that had lots of girlfriends? Lesswrongers analyzing things up the the 0.000%th? I have a general dislike for expertise in certain fields such as this because I often instinctually either agree on stuff I haven't thought about or basically say "oh I know this already" when certain "experts" speak. Not going to discount their effort but I think it's less about the experts and more about people doing stupid stuff.
Also the whole dating thing is broken because it's too structured. I say that a proper date should be like having a map that even if it's accurate you only know the terrain but you still don't know what you'll encounter on your way so it all depends on how well you click with each other. If you feel it's going nowhere just call it quits. Also helps with the silent types if you can read nonverbal actions well enough.
Blech. You don't need to apologize for yourself! Just leave it implied that if you're exchanging contact info, it's with the goal of meeting again. At most, you could say something like, "I think you're a really interesting person/I'm impressed by about you, maybe we should hang out again" - if she's not into you, you're not going to change her mind by persuading her. Just deal with that, it's part of the game.