How do I approach a coworker that I've essentially ignored in the month that she's been there?

So we got a new girl at work recently, but because we are in different departments, I can't speak to her very easily without going out of my way and looking needy. The only thing I've said to her is "Have a good night." She responded saying "Thanks, you too!" while smiling, then quickly looking down.

I feel like I've missed that initial window of attraction.

What are your thoughts?