I was in your position, and this was only after a year and a half of going out. You have to accept the fact that you said what you said... no matter what she did. Make sure she knows that you're not proud of what you did. My girlfriend came back to me and I treated her like gold. The only problem is we're on a hiatus now because she thinks I treat her too good. Strange... Anyway, the point is, let her know that you take full blame for your actions. If you really believe that you've changed, so will she. Girls like to take time though. This probably doesn't help, but I've been in that situation and thankfully came out of it successfully.