Well, at least you admitted that you cheated. And you're not being a punk like those people who say "omg! I was drunk, it was an accident". There is no "accidental" cheating.
Congratulations, you're up a few rungs on the piece of shit ladder.
Now, if you want to stay with her, tell her. If you're serious, tell her it was a one time thing and won't happen again (AND THIS IS ONLY IF YOU MEAN IT. Don't lie like a piece of shit you've established yourself to be, you're still redeemable, not a totally lost cause). Just don't be surprised or expect her to take you back.
DO tell your girlfriend if you care about her and not want to relieve your guilt, being drunk only brings out the things you would do but don't have the balls to. That's not an excuse, if you're not ready to be 100% committed don't be in a relationship.
You should tell your girlfriend the truth. You should take time to think about why you cheated. Drinking lowers your inhibitions; it doesn't change who you are or what you want to do.
If you aren't ready for a committed relationship, then take the time being single to reach that point. If your relationship isn't meeting your emotional needs but could, then that requires work on both sides.
She may not forgive you, but it's probably better than living with a guilty secret, especially one that could come to light some other way in time. Isn't it better that you show her enough respect to tell her yourself?
We're all human and make mistakes. You should ask yourself why did you cheat. Why did you even allow yourself to be put in that situation? Perhaps you'd rather be single and be free. If that's the case, then break up. If you truly do love your girlfriend, then be honest with her. Tell her you love her and spoil the crap out of her. Still, give her her desired space to grieve over your infidelity. It's OK for both of you to take time alone to think. But don't say nothing like "we should break up because I don't deserve you." ... I hate that crap.
Tell her, say you're sorry, and prepare yourself for the fury and breakup that may follow. And for the love of god, do NOT say you were drunk like it's an excuse. It's not. In fact, don't say anything as an excuse for cheating. You fucked up real bad, and you gotta deal with it.
Pay the price she deserves. Tell her. You broke the trust. I personally don't judge. It's not my place to denounce you or wish you harm. You made your choice, you must live with the consequences. Good luck m8
Do her the biggest favor and leave her. Drinking is the most pathetic overused excuse, and you should feel awful. Never would I cheat on my girlfriend. A lot of men still seem to be fucked up in this mindset of cheating.
Feeling aweful is good, that means u still love her. But u made a mistake and she has the right to leave u and finish yhis relation so i would loce u to tell her because living with this mistake is a disaster.