Thoughts...

[D3nz]

I went for the message and gave my cellphone number.

The reason is that I would prefer to chat and be able to describe myself and have it more social, compared to her receiving an invite and then accepting and then being able to view my whole history of pictures etc.

Surely it would be more engaging if we chatted over a messaging platform and I was able to tell her more about me, describe what I like etc - instead of her reading it all without interaction?

There could be so many explanations...maybe she didn't see the message, maybe she saw it and she's not interested, maybe she saw it and she doesn't know how to respond, maybe she's playing hard to get...why torment yourself? As Nick says, if they know you and they're interested they almost always would accept an invite. You've sent the message, she hasn't responded...if you send an fb invite now you run the risk of coming off as 'desperate'. Up to you though, just my 2c.