I grew up in the Philly area, and went to private schools. I think that it is a state law in PA that all school children are provided with transportation to and from school, (within a certain distance) the only problem is the logistics are left up to the local public school transportation contractors.
For instance, when I was in primary school, we had enough kids to fill a bus, so that worked out great. BUT when I was in High School, we rode the bus with the public school kids, waited on the bus while they all got off at the local high school, and then stopped at 2 other private schools BEFORE we even got to my school. I got on the bus at 5:50 AM, and got to school at 7:45AM. After 1 week my parents gave up on bussing, and drove us when we didn't stay over at school (it was technically a boarding school, but we lived so close)
It was unbearable as a teen, so I can't imagine making small children sit through the same thing.
My suggestion is to get the school involved as your advocate. That way they can also speak from the experience of other families, and it seems less like a "you vs. me" sort of thing. Also, the school should be involved because the children have been delivered late repeatedly, and that is disruptive, and certainly not within reasonable expectations.
As for the bus not showing up at all, the explanation they gave us just wrong. I can understand not sending a bus after maybe calling the school and confirming that there was no need for transportation, but to just strand the chidlren, that is wrong!
Maybe I am just rambling and not being much help, but I hope that this can get worked out. It is frustrating!