I would own up, explain that you were out of your depths and you were drunk / whatever and apologise your ass off, you will feel better for doing it, even if she chooses to end the relationship over it then you'll be better off that way and she'll know that you are more trustworthy in that you were honest about your mistake.
You'll be eaten alive by the guilt if you don't come out and say it to her, even if your relationship continues for life... it will always be in the back of your mind, afraid that the girl will say it... afraid if you are ever drunk with your gf that you'll say it by accident, you wont be able to really ever relax with it on your mind.
Honesty is all you got really , if that ends the relationship, move on, there is plenty more fish in the sea.
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