Is it sincere to apologize to a girl with a 90 degree bow?

I think it's very sincere, but I don't think people who don't know will think it's a little bit pretentious. It's a little bit, too much of a show. I'm kinda wondering why the need to bow and apologize at 90 degrees was necessary, and what exactly was the mistake. Oh, but that said, it's part of the heavy ritual, I remember when I attended a funeral before, I also bowed 90 degrees to show my respect for the deceased. In fact, I think a real apology, as long as the other person can appreciate your sincerity, that is enough to apologize.