[23M] seeking advice on how to apologize to a former classmate [22F]. We haven't spoken in 1 year.

I (23M) am seeking specific communication advice regarding a former classmate (22F). We saw each other for a few months a year ago, but we stopped talking after a disrespectful comment I made. She is now in a new relationship.

My goal is to send a final, sincere apology to take responsibility for my past behavior, without any intention of rekindling a friendship or interfering with her current life.

I would like to get specific advice on the following questions:

1. What are the best linguistic structures to use in a message to ensure it is perceived as a "closed" apology that explicitly requires no reply?
2. In terms of social etiquette, how can I clearly phrase my message to show absolute respect for her current relationship boundaries?
3. Which specific words or tones should be avoided to prevent a message after a year of silence from being perceived as intrusive or "creepy"?

tl;dr: I (23M) want to apologize to a former classmate (22F) for a past mistake. I need help wording the message so it is respectful, final, and does not demand any interaction.