Yeah, busses carry people, not cargo.

Yeah that's a fair point, I wonder if is not possible to have something like a Mansfield bar but independent of the passenger zone.

The bus is tall for two main reasons. First, to avoid getting high-centered on bumps. Since the rear wheels are fairly far forward on the bus, and the tail sticks out behind them so far. Notice that on a semi trailer, the wheels are near the very back of the trailer:

Think about how steep a slope would need to be in order for the back tail of the trailer to scrape the ground. Even with the Mansfield bar shown in the image, it’s still an extremely steep slope, right? Just eyeballing this image, it looks like about 30° of difference, which is an absurd “the truck would never even realistically be driving on that” slope:

Now let’s compare that to a bus:
Notice that the tail sticks out behind the wheels a lot farther? And notice how the tail would hit the ground on a steep driveway or rail crossing a lot sooner? It only looks like about 10° of difference before the tail hits the ground:

The tail of a bus can easily land on top of a steep hill (lifting the rear wheels off the ground, and effectively immobilizing the entire bus) if the tail is too low. Or more commonly, the rear wheels will get stuck in a dip (like a rain gutter) while the tail and front wheels are on the ground.

“Just move the rear wheels back, so the tail won’t land on anything” I hear some people starting to type out. Except that would inevitably prevent the bus from making necessary turns. Busses need to be able to fit into residential areas to pick up and drop off kids. Residential areas tend to have narrower streets, more street parking, and tighter turns. Semi trailers don’t need to fit into those smaller side streets, and are okay with a wider turn radius. So semi trailers are able to keep the wheels way back at the end of the trailer. But since a bus needs to be able to fit into those tighter residential areas, they need to have the wheels set closer to the front of the bus, so they can make those tighter turns.

The second reason the bus is tall (and I’d argue, the most important reason), is that lowering the bus or reducing the mass would increase the risk to the kids inside of the bus. By allowing the car to slide under the bus, a lot of the kinetic energy is distributed vertically, (picking up the tail of the bus and pushing the rear-ending vehicle down) instead of directing it into crumpling the back of the bus. Because the back of a bus has very little room for crumple zones. The back seats are essentially right up against the rear wall of the bus. If you lower the bus and expect it to crumple, you’re going to crush kids. And if you lower the mass, you’ve just given 60-70 kids permanent whiplash because the bus was pushed too hard. A pragmatic vehicle engineer who remembers their humanities courses could easily argue that the design shouldn’t intentionally shatter twenty kids’ femurs (and give every kid in the bus whiplash) just to save one negligent driver’s life.

Modern school bus designs are basically the culmination of engineering for a very specific set of requirements: 1) keep kids safe, 2) be able to fit into residential areas so the bus can pick up/drop off near the kids houses (which helps keep them safe), and 3) avoid getting high-centered on anything. And “keeping people who rear-end it safe” wasn’t on the list of requirements. A Mansfield bar at the back of the bus would defeat at least one of those requirements, by making high-centering much more common. The needs of the many (the kids) outweigh the needs of the few (the rear-ender) in this case.

Ok be real, we're taking about the USA here, they're not going to reduce the mass of anything.