Background
I met this colleague (let's call her Alice) at my new job that I started recently. We work in different teams, so I don't get to meet Alice every day, although I do see her in the corridor or the pantry during breaks. I usually smile at her and greet her. But I never had the opportunity to have a conversation with her since she would be out with her colleagues or on the phone and I wouldn't want to interrupt.
I have noticed that she tends to not talk very much with her male colleagues in the office unless spoken to, and hangs out with her female colleagues most of the time. She is not comfortable acknowledging me when she is with other people, so I don't greet her when she is with people or when I am around people myself.
The timings of our break from office work are quite different, hence I am not able to talk to her consistently. I don't want to coincide my break timings with Alice's, as that is not something I am comfortable doing and would make my intentions blatantly obvious.
I am in India.
Question
I am interested in asking her out eventually, but before I do that I would like to get to know her a little bit (find out if she is taken :) ) and warm her up to me. I may have to go to her work station to ask her, which brings me to my question.
How can I ask Alice to spend time with me?
Would like to point out that I want to keep this interaction between us completely casual, so she wouldn't think much of it.
I have had prior interactions with Alice, but they were very short greetings with a "How are you?", since we pass each other in the corridor. I just would like to invite her to have a longer conversation with me.
I would like to clarify that I am not trying to ask her out after these short interactions previously mentioned, because I fully well know the outcome and I am aware it's completely inappropriate.
What I am trying to get at is how I can have longer interactions with Alice at work, where it is harder to approach people. Also, only if I feel that we share common interests will I proceed to ask her out.