My four year old ds and I take the bus everyday to get to his school. Altogether our daily ride takes just over an hour (on a good day). I've been using public transportation for 20 years and I have never been in accident. My opinion is that public transportation is even safer than car travel, as long as the child can stay seated properly on his or her bum. When ds was a toddler however, he didn't quite understand that he had to be still on the bus. He fought tooth and nail to be given freedom to wander aimlessly through the ailses of the bus...obviously I wasn't going to allow that to happen, so I avoided taking the bus until he was old enough to be still in his seat.
Most strollers these days are so huge that my local transit company has banned passengers from boarding the bus with a child in a stroller during peak hours. This is a real concern for some parents who want their child to be restrained in a stroller for the duration of the ride. There were also boarding issues because one mother here tried to sue the transit company after unsuccessfully deboarding the bus with her stroller open with a child in it. The stroller fell out of the bus. I'm torn on the issue. It's a double-edged sword - having strollers on the bus is dangerous (boarding/deboarding, people stumbling and tripping over them trying to get by, etc), but not having them is dangerous too as alot of parents feel their child is infinitly safer while restrained in their stroller for the whole ride. It's a moot point for a child who is too big for a stroller though. As someone pointed out, there is no way to restrain a booster seat on a bus as there are no seatbelts.
I'm sure your four year old would be fine on the bus!
