I wouldn't say a child is 100% safe in a bus without a carseat, but they are much safer than in a car without one.
The National Highway Traffic Safety Administration reports that school busses are 70x safer than consumer vehicles (measured in fatalities, adjusted for miles travelled) despite the lack of seatbelts. That's not a perfect proxy for Mears coaches, but it's close enough - and the effect huge enough -to be a meaningful point of reference.
It's mostly just physics: busses are huge, with lots of mass to absorb an impact, and typically with features like shock-absorbers built into seats to protect passengers. They're also highly visible and relatively slow. So they are less likely to get into accidents, and when they do they are less likely for that accident to be injurious to the passengers.
If a large pickup truck crashes into my little car at 40mph, it will do some serious damage. If that same pickup truck crashes into a Mears bus, the bus and its passengers will probably be fine. The biggest risk would be if the force was enough to make the bus actually tip over, but that's really rare. They're just too big, with way more mass to absorb the impact.
