Hi,
Edit: this is a long post, wanted to put some info on how school buses versus city buses are designed to give you the information to make a choice for your situation.
City buses and school buses do differ. School buses are built with the idea that protection to the occupants is provided through compartmentalization; occupants aren't restrained per se but are kept from serious injury by padding the surfaces around them. The seats are high backed, padded and spaced close together (and there's a padded back in front of the front row of seats). They are energy absorbing, and meant to give a bit when the occupant behind strikes the seatback.
Now compartmentalization works best for kids 40lbs and over; kids below 40 lbs are recommended to be in child seats.
The structure of a school bus is also built to very high standards to ensure it maintains its integrity in a collision to protect occupants. Its also designed to prevent ejection from the vehicle; this is why school bus windows are small openings.
If you want to clarify what that means in real life consider pictures of intercity buses after serious collisions, and then pictures of school buses; after nearly all collisions, the school bus still looks like a school bus but intercity buses (and other passenger vehicles!) often look like a large pile of crumpled aluminum foil.
And finally at least up here I live/grew up school buses use diesel instead of gasoline because diesel is far less flammable in case of a collision.
City buses, as well as intercity buses, aren't built to the same standards as school buses. The seats are often hard metal or plastic, not designed for compartmetalization, and the windows are large, not designed to prevent ejection.
Now I speak from experience growing up as a child in a large city and taking city buses all the time with mom during the day when dad took the car at work:
Never once was I ever on a bus or streetcar that was involved in any kind of collision, not even a bump. You hear very rarely of accidents involving public transit. And in the case of public transit, I do believe that if they happened you would hear about it in the news. My growing up years, imagine how many kids' parents cars were involved in collisions?
And the only collisions I've heard of involving injuries to the passengers on a city bus was a couple of years ago, and the reports were the driver was weaving all over the road, and was suspected to be smoking marijuana and drinking beforehand.
So I wounldn't worry about being on a city bus at all. Intercity buses concern me more. They
seem to have more serious collisions, probably at least partially due to higher speeds. If the vacation shuttles operate at higher speeds, more like intercity than local city buses, that would concern me. Also, lately some companies have been equipping intercity buses with lap/shoulder belts for passengers. If the shuttle buses have been equipped with lap/shoulder belts, in my opinion the occupants should be restrained and I'd want my child to be in a carseat. I've never heard of a city bus having seatbelts and can't imagine that being done.