Pardon me for saying so, but you've got it all wrong.
Pardon me, can you direct me to the train station?
A: Dad, can I talk to you?
B: Of course, Sweetie. What's up?
A: I need to apologize to someone and I don't know what to say.
B: You should be direct, use their name, be sincere and say that you regret what you did or said. I always say"I owe you an apology".
A: But what if they get angry?
B: Most people are forgiving, so there's no need to worry. In fact, if they can't find it in their heart to forgive you, they're not very nice people.
A: Thanks, Daddy. You've been a great help.
B: Anytime, Sweetie. So who do you need to apologize to?
A: You, Daddy. I'm so sorry I scratched your new car with my bicycle.