I like my co-worker, how should I talk to her?

Okay so my co-worker is 25 and I'm 30. She is so beautiful. But the problem is she is kind of on the cold side I'd say. We are both teachers but I rotate between two different schools. I'm a music teacher and she's a third-grade teacher. I want to get to know her more but it's hard. On the first day she started teaching there because she was fresh out of college, she was in the teacher's lounge on her cellphone. After she got off the call, I said good morning and did a friendly smile. She just good morning coldly. As we were making some coffee, I asked "How are you?'' just to make small talk. She just said "fine" and then walked off. She didn't say it in an angry "go eff yourself" way, but she said it shyly. I tried to get to know her better by just observing her but she's so reserved. I mean she doesn't mind sharing her opinions on how she feels, but when it comes to her life, you can't figure it out by looking at her. Yes, I know you can't figure someone out by observing them, but I just wanted to see the simple details or at least try. One day I was in the principal office waiting for some papers. My principal asked If I could've run them to her class to sign and I gladly did. I was pumped this was finally my chance to maybe talk to her. On my way to her class, I was just thinking of things I was going to say to her. When I got there I knocked on her door. As she was packing up her things I told her that the principal wanted her to sign this. She didn't say anything and she looked at the papers. As she did that a whiff of her perfume and her smell hit my nose and I almost melted. She made me nervous. I couldn't concrete so I said thank you and left the room. She started working here last year in August. Ever since then, I say I'm going to talk to her but I get nervous and shy. So, now that we know or at least have an idea who she is, how can I talk to her and try to get to know her better. I was maybe thinking of asking her out for coffee? What should I do?
I like my co-worker, how should I talk to her?
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