[bombcar]

I suspect if there are variations on "amount of bullying" it comes down to culture rather than "school uniforms" - at least one Japanese manga is all about bullying in a school uniformed school, so it must happen enough to be a bit of a trope.

It may happen less in places where the private schools can be school uniform or not, but there I suspect it has more to do with expelling the bullies than anything to do with the uniform itself, since it won't usually cover other status symbols that can be obtained (shoes, hair decorations, etc).

That's not to discount that the uniform may be useful for various reasons.