Dear {Mr./Ms. Last Name}
I deeply regret my actions on {day of week} and would like to offer my sincere apologies for the incident.
What I did was inexcusable, childish, distracting and disrespectful. You, as well my fellow students and {school}deserve better from me.
In the future, I will practice more restraint and professionalism so as not to repeat the lapse of judgment I displayed.
I value your commitment to instructing and guiding me to success. If you would like to discuss this further, please don’t hesitate to let me know.
Sincerely,
{Student}