Need advice!

I have been chatting online with a girl for over six months who is four years younger than me. We talk once or twice in every week from midnight to morning. She is kind of a conservative girl which is why I didn't bring any topic about relationship to her. Day by day I'm getting emotionally more attached to her and almost always thinking about her. As I am shy and didn't ever have a girlfriend(It's awkward I know!), I don't really know what do to, and how to tackle these facts. Frankly saying, this situation of confusion is pissing off my daily life and work. The reason I can't ask her to meet directly is my fear of getting rejected and then we might not be having those wonderful weekly conversations.

What should I do now about her?
Help! :(

And thanks for your time.

You can either ask her on a date or continue on a downward spiral which is causing you to be more unhappy each day.

Your choice.