So I think part of the problem is, 1, misunderstandings. You two have different ideas of what "getting to know someone" means. To her that is emailing/texting etc, and to you it's getting coffee. At least in this context. 2, You seem a bit too keen for coffee, and now, with someone who takes things slow and has a different communication style. 3, She's uncomfortable about the age difference.
She sounds like me in certain aspects. I do have very little friends, however...and I don't think I'm great at communication so I don't know if I have good advice?
But I also prefer talking online and it takes a lot for me to hang out with someone mostly. Also you started to sound like a difficult person to chat with. Mostly here:
You said, "I'll move on" like this was something dramatic, when you only met her a few weeks ago. Then you confirm that it was in fact a big deal to you by implying that this could start drama at work. Comes off as clingy to me. If I was her I'd be hesitant to reply back to that as well, or I won't reply back at all (Not proud of this, but I do often do it when I feel someone is too clingy, I'm personally very sensitive to it).
& You told her that you would see how she felt about the coffee thing in a week or two? I personally wouldn't like it at all if I was being measured like this. To me it sounds like a due date. If I don't feel like getting coffee by that time then (blah) happens. I'm very go with the flow. Not to mention that to me two weeks is like a day. And it also takes me a long time to warm up to people as well. Maybe I'm missing something...I do think I'm difficult to get to know but meh...I understand her just fine?
She sounds like me in certain aspects. I do have very little friends, however...and I don't think I'm great at communication so I don't know if I have good advice?

First of all, I didn't see her say that she won't ever hang outside work with you over coffee? Just that she takes a while to warm up to new people, so she prefers chatting via email. I think that's perfectly reasonable. She might even have social anxiety/or is just shy. It sounded like you were cool with that, but now you say this, which sounds a bit strange. Unless I'm missing context.
You said, "I'll move on" like this was something dramatic, when you only met her a few weeks ago. Then you confirm that it was in fact a big deal to you by implying that this could start drama at work. Comes off as clingy to me. If I was her I'd be hesitant to reply back to that as well, or I won't reply back at all (Not proud of this, but I do often do it when I feel someone is too clingy, I'm personally very sensitive to it).
& You told her that you would see how she felt about the coffee thing in a week or two? I personally wouldn't like it at all if I was being measured like this. To me it sounds like a due date. If I don't feel like getting coffee by that time then (blah) happens. I'm very go with the flow. Not to mention that to me two weeks is like a day. And it also takes me a long time to warm up to people as well. Maybe I'm missing something...I do think I'm difficult to get to know but meh...I understand her just fine?
