Before you ask her to be your girlfriend, you should find out if she feels the same way about you. I don’t think there is an exact number of dates to go on before you ask. If you feel that she likes you too, the way you like her, then ask. Do it at a time when you feel comfortable and ready. Make sure that you’re ready for a relationship though as crossing the line between friendship and dating/relationship, the way I see it, it’s kinda dangerous going back and forth. You don’t want to lose a friend if it doesn’t work out. So it’s something serious to think about.
I don’t think there is a certain [b]way[/b] to ask a girl to be your girlfriend. Every guy has a different way of asking. Over a fancy dinner, or on a romantic date walking along the beach, there are many ways. For me, when my boyfriend first asked me to be his girlfriend, he asked me when we were talking on the phone. I was on vacation with my family out of town at the time so it was a long distance call. He wanted me to be his girlfriend and I guess he didn’t want to wait until I returned (thought I still don’t know if that was the reason to this day!), so he asked me over the phone. That made it one of the happiest days of my life among all the other happy days. I think that the best way to ask is what you feel is most comfortable when you’re with her.
Since your birthday is coming up, you could do it then, if you want to make it memorable for you. It depends on you. The best time is when you’re comfortable and ready. My b-day is the same month as you lol. 🙂