How many times have we said, “I’m sorry, I didn’t mean to bump into you, or I’m sorry, I didn’t realize you were in line, or maybe, I’m sorry, I wasn’t paying attention and I didn’t see you.” Does it sound like we are truly sorry and sincere for what happened, or are we just saying words, or is it just excuses for what we have done?

Yes, we can say we are sorry for something we have done and mean it, but the power and sincerity can get lost in the encounter. We all do things we are sorry for, but I would offer a more powerful way of getting your apology across to the person, and leave a lasting impression with them, that they may pass on to others.
Why not give them the power of forgiving you for what you have done, rather than you making that decision or statement. By simply saying, “please forgive me, I did not mean to do that to you,” shows your sincerity, and quickly gives them the decision power to make a determination and say back to you, “that is ok, no harm done.” That person will feel empowered and moves forward in their day feeling a little better about themselves and the situation. And you? You can walk away knowing you did the right thing and made a difference in their day, and a lasting impression.
_Conor