One thing I have been able to compare when it comes to school to regular buses today is that the school routes have a lot more pressure on running it. For example, there is a risk that you can get in late to school. As a school student, I have been through this and I personally see temporary traffic lights are just too bad and time consuming (this happened today).
The big difference here can be 'a normal local bus route which just so happens to be used by school kids' and 'council pays for seats on a local bus route'. The latter has just as much pressure to run it because there are penalties in place for not running it. This style of working also means that there is generally more capacity too as the council may ask for 50 seats say, a double decker is put on which means at least 30 seats for school kids who need to pay (if there is any demand for that, it depends on the councils policy on free school transport) and normal members of the public.
On regular buses, students relying on them is kind of inconvenient to the regular people as they will just fill it up to the brim. In addition I have seen this happen multiple times before.
Again, this depends on the style of service but also depends on the operator. Professional operators will ensure that there are enough seats for everyone. Unprofessional operators and those who are just dying for an extra few ££ in their back pocket will not care and will want the bus at it's legal capacity (which for some deckers is 100), and not care for passenger comfort.
It's all down to who runs the service really and what, if any, contracts they have with the council for conveying students. I have a Stagecoach route in my area using normal Scania E400s, standard Stagecoach spec vehicles, there are 67 spaces paid for by the council and the capacity of the bus is around 80 so based off everyone having a seat, that is 13 seats for the public. In reality of course some kids choose to stand, I am not sure if the capacity on Bus lists on the web included tip up seats which could give more capacity. There's a few other variables. Either way, based off them numbers, there is enough capacity for both normal people and school kids. I know, and have seen some less reputable companies shall we say running though on routes which carry 100 kids on a 80 seater bus. All varies. There's good and bad examples.