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Worth a shot?

I like a girl from work who I've known for a couple months now. She's 3 years older than me (not that it matters to me), and we've become friends. She's not my usual type as she's quite shy (I would describe myself as outgoing and good looking, pretty good at sports and always been fairly popular), but that's probably part of the intrigue. It's really hard to tell if she's interested, she's crap at texting to say the least (has admitted as much herself) but sometimes she'll just leave me hanging in a convo (not flat out rude, more she'll not reply to a text that doesn't really require a response but you'd expect most people to reply to). In person she's we can have a laugh but once again she's generally quiet (especially in a group of people), I always find myself having to coax convo out of her and she comes out of her shell a bit more. Almost like she's embarrassed to speak with me (although it could be because she's shy). Someone at work made a joke about me being entranced by her in front of her, and a few others sniggered which makes me think they've talked about it (she stayed quiet but maybe could've talked about it behind my back). I've been "out" with her quite a few times, like met her for lunch where it's just us two and stuff, although this wasn't necessarily considered as dates, she could've seen it as two friends. She does say yes to these "dates" so she must like me a little I figure, but then maybe she literally sees us as friends and nothing more. Last week she was going shopping after work and I said I'll come with her, she said 2/3 times you don't have to, I made a little joke asking if she wants to get rid of me and she said it's not that, but could this have been her basically saying leave me alone? I've tried kinda flirting but she doesn't seem to show much either way. I think she might know that I like her, I'm fairly sure I've made it obvious (when we were walking back, made a joke about not liking her and she said is that why you've followed me around for the last 40 mins, was in a jokey way but could that be how she sees me? As an irritant)?Here's the tricky bit. The nature of our work means that basically from now until the foreseeable future we won't see each other at all, or at best a couple times a month. I'm considering asking her to a date this weekend, and just laying all of my cards on the line. What do you think? Is it better to basically say how I feel or just ask her for dinner or something but in a way she knows it's a date? Or do you get the impression from what I've said that she doesn't like me in that way. Was in a office meeting the other day with her and there were other guys on our table and the thought of any of them liking her/getting with her made me feel sick. Thoughts please.