Try not to get hung up about bullying, it's human nature and a school with less bullying does not exist or is lying if it says bullying is not in their school.
If you want good pastoral care, I came to the conclusion after visiting several state boarding schools that the ones with the higher proportion of boarders V day student and the ones with the higher proportion of full boarders V week boarders were the schools were I preferred the pastoral care on offer. I disregarded all schools which were too far to travel to. I disregarded all schools where boarders made up less than 1/3 of total students. That left me with about 5 schools to choose from. Then I chose the one which "felt right". I think myself very lucky. My son has had the best 2 years of his life and the pastoral care is just without criticism from me, I could not ask for more.
If I did it again, looking for boarding accessible from mainland Europe, I'd look at Sexeys, Old Swinford, Gordon's, Holyport, Cranbrook, Duke of York's. And Hockerill for my bilingual children.