The OP is unreasonable expecting school staff to look after her child.
she didnt expect them to, due to unforseen circumstances, a one off, a bit of bad luck she was late, things happen unless your as perfect as katie, i have used public transport all my life, sometimes, not often the buses just don't show up, what then? You can be there on time for it but if it doesn't arrive then your stuck unless you have a 10 min regular bus service and can catch the next one, should she get a bus an hour earlier with a baby in a buggy and wait for an hour in the playground, what about in winter when its freezing and lashing down rain, what then, someone phone's SS because your standing in the playground with a baby freezing because you got the bus an hour earlier just in case it's late again like that ONE time it was.
It was a one off, she's never normally late, the bus is normally on time, for whatever reason (breakdown, someone collapsing etc etc) the bus was late once, she was late, once
I am pleased all the teachers at our school are really nice, helpful people, im sure if i explained the above ^ they would be fine as it would be a ONE OFF so they would know something had happened as i always collect on time, they would help me out, not scold me in front of my child
Surely the teachers know who the persistent offender's are and deal with them appropriately, surely they realise if you have never been late, you have rung and told them your in difficulty then that's unusal so can help by sitting the child down with a book or some pens or if they have to go asking someone who's not going if they can keep an eye on them because it's a ONE OFF