First thing you have to do is apologize to her. Tell her you should never have hit her, this is a must if your relationship is going to survive.
Then sit her down and tell her that the way things are going now it will be impossible for either of them to carry on this way. I know it is hard but I recommend you take a small break, say 2 weeks away from each other. I would let her have your house or wherever you live to show you are really sorry about hitting her (which you should be).
A break should cool both of you, and than you could ask her out to a restaurant 2 weeks later, tell her how you feel. 1st things 1st, you have to make the first move and tell her your sorry.