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I think the easiest thing with a coworker is to ask her to lunch. You can do the "Hey, I'm going to go grab some lunch, want to come along" thing. Lunch is light and it doesn't have to be a big deal. If it goes well, you can say "Hey, this was fun, would you be interested in <insert other activity here>?" Dinner, a movie, a party, whatever. That way the whole thing isn't heavy with importance and tension.
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