The first thing you should do is try to convince her that you are truly willing to change and that it will never happen again. If necessary, you may need to stop drinking, since alcohol and going out to bars were part of what led to the situation.
Do what you can to show her that you’re serious, so she can slowly start trusting you again. But of course, we still can’t know if she will forgive you—so for now, just do everything you can to make things right.