Dear {Recipient},
I would like to apologize on behalf of my {Type of Animal}, {Name of Pet}. As I'm sure you understand, my {animal}did not maliciously attempt to {incident}. As the owner, I take full responsibility for the behavior of my pet.
I have taken steps to ensure that {incident} will never happen again. As no one was injured and all the damages have been resolved, I hope we can put this incident behind us.
Again, please accept my most sincere apologies for my pet's behavior.
Yours truly,
{Sender}