Hitting you was not a great move on her part but I think her anger was justifiable. It is unfortunate though she took her anger to a physical level.

There are lots of questions here to deal with before getting back together the least of which is her forgiving you. But first, you need to show a sincere acknowledgement of your mistake. This includes not just the act itself but the decision to initially deny it. I speak from experience as I have been there with previous relationships before. An apology was not what I wanted rather an acknowledgement that the act was both wrong, hurtful, and that I was not the cause of it. Without this, the apologies meant nothing to me and I harboured then a resentment which only grew and grew. These relationships never got past that.

I wish you good luck. With some work you two may be able to salvage things.