I am writing this letter to express my sincerest apologies for [reason for apology]. I understand that my actions have caused inconvenience and disappointment to you, and for that, I am truly sorry.
I take full responsibility for my behavior and I assure you that it was not intentional. I deeply regret the pain I have caused you and I promise that I will take every measure to ensure that it never happens again.
Please accept my heartfelt apologies, and know that I value our relationship and your trust in me. I hope that we can move forward from this incident and rebuild our relationship on a stronger foundation.
Thank you for taking the time to read this letter, and once again, please accept my sincere apologies.