First forgive yourself for essentially cheating on her. If you don't forgive yourself she will eat you alive in your new relationship. She will continue to bring up your mistakes and make you feel guilty.
From there comes honesty. Tell her because without honesty there is no relationship. She will know something is up because you will be a little bit off. She might not be 100% sure of what is wrong but she can tell something is wrong. She will use her mind to search for reasons why you are off and cheating will be the first thing she jumps to.
After honesty comes her forgiving you. If you don't forgive yourself your apology will come from a place of weakness and begging to be forgiven. This weakness will cause her to lose attraction for you because weakness is not very attractive quality to have.
Before anything I would try to figure out why you wanted to cheat in the first place. Is it in your nature or did she help in you trying to cheat? Maybe the relationship wasn't right to begin with and this is why you decided to stray? I'm not putting a right/wrong judgment on cheating, I'm looking for you to find the answers why this happened.
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