Remember that the other children will be somebody else's beloved dd or ds, and they may well be afraid that your dd will be horrible or catty to their little one.
(and hand on heart- can you be sure she never will be? children do go through odd phases)
schools are not the only places where bullying can happen, it is a risk you take if you let your dd associate with other children at all, anywhere. In my experience, though, many schools are very good at dealing with it and I have learnt a lot from dc's schools which has made me a better parent.
I know I have posted frequently about some problems we had with dd's junior school. But then I have also posted frequently about the problems we have had with dd's disability and with her being misdiagnosed by the local hospital: this does not mean that everybody who has a baby can reasonably expect that it will be disabled or that anybody who sees a doctor should expect to be misdiagnosed!
The infant school and the secondary school could not have been more lovely- and most of dd's friends had a lovely time at the junior school too.
Both dc have made lovely friends at school, dd at 16 is still best friends with the girl she played with at infants, both have liked their teachers, any issues with bullying have been resolved swiftly and efficiently by the school.
Like you, I came from abroad and was dubious about the British education system, but I have been very pleasantly surprised. Dd doesn't know exactly the same things as I knew, or valued, at her age, but I can see how her learning is benefitting her. I found I could enhance dc's learning experience by trying to help them to see how what they did at school did have some ultimate purpose.