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I would like to ask her to lunch or something, but our work schedules are spaced quite differently, and being that I haven't spoken to her much at all asking to lunch would seem a bit premature?
Ok I want to take your post out of context to give you some perspective. Lets say for fun you are a guy who is sexually premature.
So what?
I know there are a lot of guys who would make fun of you. I wouldn't. Did you know that most healthy relationships consider sex as a bounus? Did you know that most healthy relationships are based on commonalities?
She is probably guarded up against you because you have the wrong set of mind. That's probably why you can't talk to her. It has nothing to do with what you say, but how you say it.
Sure you can learn these line, but your not in a bar. You are at work. The lines will only make you seem creepy. Work girls don't want their co-workers hitting on them.
My advice to you. Make her your friend. If you don't get any then oh well. The more reliant you are on sex them more creepy you will come off.