What does "take a chance" really mean here? Why does the bus driver take a chance on a student?
To "take a chance" here means to risk trusting someone. So in this case, he means that the bus driver "took a chance" on him by letting him on his bus even though he didn't know who he was. Even though public buses allow anyone to ride the bus, sometimes bus drivers know the passengers and are more comfortable around the passengers they know who board the bus. Here, he is referring to the fact that he took a bus that was the wrong bus and made him late to school, since the bus driver didn't know him.