If you want to say "Thank you for your patience", don't say "Sorry I'm always late".
I've really taken this to heart. I rarely say sorry anymore.
Apologizing always felt weird to me. My dad would sometimes make me do it. Would make me apologize to my brother, for example. I never quite understood it. How does the apology make things better? I did what I did in the moment because it was the best I knew how to do. Maybe I know better now. Same when someone hurts me. I know they did what they did because it was the best they knew how to do.
Apologizing, it seems to me, is mostly for the benefit of the person apologizing. I apologize so I feel less bad about having done whatever I did. When people apologize to me, I don't feel better for it. It feels like a distraction from figuring out what we'll do next, together.
When you apologize, you're putting the other person in a tough situation. It's understood that they should probably say something to forgive you, to say it's no big deal, it's okay. Or they can double down and say "yes, that really sucked". Then you can apologize some more.
When you apologize, it's on them, and whether they say something nice or not, if they did indeed feel hurt or violated by your actions, either choice feels bad. You're putting yourself down, and leaving it to them to pick you back up, or let you lie there on tho floor. Both options suck.
I like the "thank you" approach much better. That makes the other person feel appreciated. You're saying you've received the gift they offered in being patient, in listening, spending time with you, whatever it is. And then they can say "you're welcome" or they can say "I'm not doing it again. Next time you're on time, or I'm gone", or whatever they need to maintain their integrity.
If I could eliminate the words "I'm sorry" from the English language, I think the world would be the better for it.
Try it next time.