Girls, I don't know how to approach this situation with this girl at work?

Anonymous
There's a girl i've known for a bit at work (few months), we barely spoke before but when my birthday passed she wished me a happy belated birthday and what did I do and what not. This guy who also works there kind of cut the convo short while she was talking to me and she's like "how rude" to him. I eventually helped another customer seconds later so it's not a big deal. What I do at work, I'm always fairly busy, I don't have time to chit chat for long periods of time. Throughout the weeks if I have to pass her department i've noticed she tried to make small talk but again, I'm always on the move and I don't want to get in trouble with management for talking.

I've realized, recently, she's fairly standoffish, I tried to talk to her about her school but I felt like the convo was cut fairly prematurely. She's more talkative to most employees in the store than me, which I don't get. I'm not a mean person and I am willing to help anyone in any department. Part of me feels like she may like me but I can tell she's dating a guy from the store. Yesterday, I was one of the last people to leave the store and I noticed her and the guy I work with in her car waiting in parking lot. They look at me, and the guy starts laughing hard... I don't know why, it could be anything but seemed directed to me. I got picked up by my mom and went home. I considered that rude to be honest.

I am not looking to be with this girl, but should I stop talking to her all together and not say hi anymore? This girl does not know me well, she doesn't know I'm doing grad studies for my Masters, she doesn't know my history, she doesn't know my family or friends, she doesn't know my social media, other people in the store don't know my social media. I live a fairly reserved life so if she's judging me then I consider that immature. I didn't do anything to hurt her feelings or make her feel weird, again I'm always busy at work in my own department with tasks I have to finish.
Girls, I don't know how to approach this situation with this girl at work?
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