Sorry I wrecked your car!
I would like to apologize to you for the accident that occurred on last July 2nd. It was entirely my fault, and though you have been more than gracious, I feel the need to extend a formal apology to you. It was absolutely an accident, but rest assured that I will be more careful in the future.
Even though my insurance will cover all the damage to your car, I know this incident has caused you stress and inconvenience. I would like to extend to you a small gift as a token of my appreciation for your honorable behavior.
Again, I am very sorry for having denting your car.
Sincerely,
Bob