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depending on how interesting she is, you can actually ask some questions that indicate you have some respect for her and would actually like to know...

have you used this icebreaker before and was it successful?

what has been your most successful relationship and was it recent enough that you are still emotionally involved?

what is the level of emotional intimacy do you expect to find in a first date? (use the word emotional intimacy and you may find out about physical intimacy more easily)

what do/don't you do for fun/hobbies?

what attracted you to me, and what are deal breakers for you?

who are some famous people you admire and why?

in your family/friends, who do you feel is closest to your ideal role model and why?

what have you done in your life that makes you proud? or most depressed? are you on track for your own goals/career/relationship desires?

what do your friends admire about you?

what is your wildest dream for yourself, or the world?

maybe all of these are a bit much for someone who is just a casula friend/date, but will probably get you to know quite a bit about her...i suggest you write the questions out on index cards, and have a lighter group and a more intense group. that way you can change courses in midstream if things seem to be going in one direction or another.