Ok if you cheated, whether you apologize or not is up to you and your general virtues as a human being. What's more important perhaps in that situation, if you want her back, is to openly explain why you did it and that the other girl doesn't mean as much to you as her. If it was just cheating for sex or for something different and you had minimal feelings it's going to be easier than if you were also emotionally cheating on her. Ive cheated before, got busted, and most of what I had to say afterwards leant towards why I did it and explaining that the girl didn't mean as much to me but it 'just happened'. I said it was hard to go from being a playboy to a committed relationship and that what happened had actually strengthened my feelings for her, realizing I really don't want to loose her. I didn't get angry and I didn't apologize - I told her truthfully what happened - that is the responsible way I think. Sometimes things happen for a reason, especially early on in a relationship.