No, I would make a plan with my child for what to do if he gets home and nobody is there. (He does not take a school bus--he walks--but we do have such a plan: Go to his friend across the street whose dad is home. If her dad were not home, she would come to our house. Odds of both dads being delayed on the same day are quite low.) If his bus were late, especially if I could see bad weather, I would not worry for at least half an hour.
I commute to work by public transit, and my partner's parents have repeatedly fretted about how can the rest of the family know when I will get home, if I can't text them updates on where I am? I don't get it--we all survived the years when technology did not make that possible! I get home between 6:00 and 7:00, usually before 6:30, but if I'm later it must be that there's heavy traffic or some other problem. If something's truly wrong, I'll call them or the authorities will, so unless that happens there is no point worrying.
Life is more peaceful when you don't feel like you have to monitor everyone every moment.
