I am writing to apologize for my unlawful operation of [vehicle/machine/etc.]. I understand that my actions were wrong, and I take full responsibility for them.
I understand that my actions put myself, as well as others, at risk and that is why I am writing to apologize for my actions. I should have been more responsible and aware of the consequences of my actions. I understand that I have violated the law and I regret my decision.
I am deeply sorry for my actions and I understand that I have caused you a great deal of distress. I understand that I have to face the consequences of my actions and I am willing to accept whatever punishment is deemed necessary.
I have learned my lesson and I will make sure that I never make the same mistake again. I will take the necessary steps to ensure that I am always aware of the laws and regulations that I must abide by. I will also take the time to educate myself on the risks associated with operating [vehicle/machine/etc.] and I will make sure that I always follow the rules and regulations.
Once again, I apologize for my actions and I will do my best to make sure that I never make the same mistake again.