I say “excuse me” to get someone’s attention if I’m interrupting them. I also use it if I’m walking or reaching in front of someone that interrupts their sight line regarding something they are doing. Like if they are looking at a shelf in the market, talking to someone, or watching a show.
I say “I’m sorry” if I accidentally bump in to someone.
I say “I beg your pardon” if I don’t hear something well and the person to repeat what they said.
I’ve seen statistics that women apologize much more often in some form or another throughout the day than men (an American statistic). I know if I compare my family to my husband’s, regardless of gender, my family is much more apt to apologize for small and large things. Much much more. A cultural thing maybe, or maybe it’s just his family.
If I bump with someone I almost never worry about whose fault it is, it doesn’t occur to me to even think about culpability, especially in a crowded place. I say I’m sorry to acknowledge the bump, it’s not really taking responsibility for it necessarily. It depends on the situation. My husband’s family equates an apology with taking responsibility and admitting you are a horrible person. They seize on it, and it feeds their own ego. Sometimes a formal apology is an admittance of wrong doing and asking for forgiveness, but a quick excuse me or I’m sorry in every day situations is often just an acknowledgement and checking the other person is ok.