Hey Zoggster,
I'm sure you know, but the more time you spend chatting online or over text, the less chance you have to gain a non-platonic relationship with a woman. I would let her know that you'd be interested in meeting her in person, and if she complies, using that as a way to get her number to simply set up logistics. However, since she seems reluctant to give her number out, it may be because she is uncomfortable around people she's never met. Therefore, offer to meet up with her in a public place with lots of traffic (a mall would be a great place) and do something where there are a lot of other people around (go to a museum or something). I would not ask for her number as soon as you get her to comply, perhaps wait until a day or two before. Here's a scenario to give you an idea of what I mean.
You:
I like the fact that you're easy to talk with. We should meet up and shoot the breeze later on this week. Plus, I've been dying to check out this new store they set up in the mall! (In this situation I would throw out a possible public meeting place to her, instead of just saying "let's hang out." This will give her an idea that you want to stay public, and would make her more comfortable in meeting you."
Her:
Yes, I think I'd like that!
Set up when you all should meet at the mall. Then the day or two before, message her saying something like this.
You:
We still on for Friday?
Her:
Yes, at the mall, right?
You:
You got it! Let's swap contact info quick, so we know where to find each other!
Going about it like this, gives her an excuse to give you her number. That way the phone number isn't about carrying on a conversation like you already do online, but rather so that way you both can figure out the logistics of meeting each other (because who's gonna bring a desktop computer with them and scan their online dating messages in the food court
Anyway, hope this helps!
CHAT