I can't get the right moment

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So the place I work I was moved over to a different shift a month ago, and there is a girl I really like. We work in a food factory, I am a machine operative (training to be an engineer/fitter), she is Quality Control (essentially the person who checks food and does the paperwork), I walk past her alot since my job involves me moving around. She has definitely noticed me, we have made eye contact and smiled at each other a few times, I seen her looking at me in the corner of my eyes so I'm kind of wondering if she is interested, or more likely she is just looking to see if i'm looking at her. The only talking we had was when she was struggling to lift something heavy and I moved it for her, she smiled and said thanks, we were busy and couldn't talk.

I think she is within my league, she isn't popular since there are other girls to hang around with and they more or less only talk to her as a "are you ok" sort of thing that girls do with each other. She seems really quiet as she always sits by herself at lunch.

From what I can tell she seems friendly, for example the disabled guy in our place always goes up and says hi to her and she smiles and talks to him, so its not like she is inherently stuck up. Also since the other guys are either too old, have girlfriends, chasing the more popular girls, or whatever reason I don't necessarily have competition.

The thing is as much as I want to talk to her and despite spending most of the day within a few yards of her I can't find the right moment to go over and say "Hi whats your name". She is always pretty busy doing paperwork, while I am either fixing machines or carrying stuff around. I feel like I need to wait for the right moment but I don't know when that could be, then again I mightn't get a right moment.

Should I just be direct, i.e. walk up and say hi or be tactful ?

What I imagine is as soon as I try to talk she has to do something then cuts me off, either because she is busy or knows what I am doing.