Simply replace the unfilled areas such as "" and "[date]" with your information.
I'm writing to apologize for the incident on [date]. I'm very sorry for what happened, and I'm sorry for the way you were affected. I have no excuse for what I did.
I'm writing to ask for your forgiveness. This is the first and last time that this will happen. Please let me know what I can do to help us both get past this.