Simply replace the unfilled areas such as "[]" and "[date]" with your information.
Dear [name],
I'm writing to apologize for the incident on [date]. I'm very sorry for what happened. This act is not part of my character, and will not be repeated.
I understand you're angry and that we'll have trust issues to work out. I'm willing to put this behind us and work toward a better future.
I humbly ask for your forgiveness.
Sincerely,
[name]