How do I tell this to my ex?

A while back when my ex and I were still together I cheated on her with another girl. We were just friends and I was spending the night at her house and her mom was in her room and we were in the living room. The power went out, we were on the couch and she was scared so I got close to her and I kissed her. We were together for about a month before I found out she was cheating on me. So I yelled at her pretty much calling her a slut. But now looking back at it I am the biggest f*cking hypocrite in the world. I wanna say I'm sorry but I don't have the guts to (she's also my ex). But the main ex is the one I cheated on. I wanna tell her. We're friends now. But I know she's pissed at me already when I told her I was an atheist. But I still wanna be her friend but this has been on my chest for years and I really wanna tell her. How do I tell her?