Fun fact: school buses in the US are legally allowed to ignore posted weight limits on bridges. While this may seem particularly insane, usually on bridges the posted weight limit is not the weight that will make the bridge instantly collapse, it's the weight that if regularly exceeded by crossing vehicles will cause undue wear and require the bridge to be repaired or replaced sooner than it otherwise would have been. School buses are infrequent enough (and relatively light enough, even despite the child obesity epidemic) that they don't create a significant problem.
On a wooden bridge like this, though, the same logic does not apply. I sure wouldn't cross it in my school bus, but the height limit would preclude that anyway.
Well, school bus bodies are a lot stronger than people think (I say this as someone that's rebuilt one as a skoolie) but so are wooden structures. I'd pay good money to find out whether school bus or covered bridge roof would win in a fight. I think the reality is that they'd both come out of it in pretty bad shape - but the kids would be fine.