Generally speaking, US school systems consist of separate elementary, middle school/junior high, and (senior) high schools with staggered start and end times for the school day to accommodate buses. For example, back in high school I think the actual school day started around 7am or maybe 7:15am or so. I'd catch the bus at around ~6:30am as I lived towards the end of my bus route; some kids would be up earlier. The buses would drop off their charges with a bit of time to spare and head out again for the next schools (in order: high school, middle school(s), and elementary school(s)). At the end of the day, the buses would line up around the school (again, for my district, maybe 15-20 minutes before the final bell and with two 'flights' of buses, IIRC), load up the kids, and head out on their route in reverse before repeating at the next schools.
It's not really an example of a functioning public transport system; it certainly works, but only in a very limited and specific context and without any flexibility. If a kid misses the bus either in the morning or after school (which can happen often), they're going to be waiting for a ride home from a family member. After-school programs required the same. And if you're in a rural community? The bus rides are longer, and you're waking up even earlier. But for a lot of suburban communities, there's no real alternative. If they have a bus system, it's probably for commuters and goes from specified stops (often from large "Park and Ride" lots) to the nearest city.
In that sense, there often isn't a public bus to put kids on in much of the US. Assuming, of course, that parents would be willing to do so. Back in 2008, a writer wrote about letting her 9-year-old ride the bus and subway to school alone.[0] There was a ton of public outcry, and she was labeled "America's worst mom" and suggested it was equivalent to child abuse. But that's a different issue altogether.
0. http://nysun.com/opinion/why-i-let-my-9-year-old-ride-subway...