Interesting about the bullying thing our friends DC left for exactly this reason. Their DC is shall we unconventional (which is why they choose it) and they are very very wealthy but not flash it around wealthy and they also found that there was a lot of stuff about personal appearance and parents status etc.
I'm finding it a bit hard to explain tribal, I know what it looks like when I see it, there was definitely a feeling of a them (being teachers) and us (pupils) as it inevitably will be in any close knit boarding school and I'm not saying it's bad but I just got the impression that the pupils were very much doing their own thing. That education in terms of exams etc was not the pupils number 1 priority. I also got the impression that there's a lot of seriously monied parents there (our friends would agree) and I accept that this goes with the territory of being at a boarding school and don't get me wrong DS2's school had mega wealthy parents but the kids were telling me how at the weekends they go into London and spend the weekend in their parents/brother/cousins flat drinking and taking drugs having a good time. I suspected those who couldn't or wouldn't keep up with this would be very much on the outside. I'm under in illusions I know this goes on in lots of big name big fee independent schools and I'm sure plenty of the Bedales pupils don't do this but there was just something about the whole thing that I didnt feel would be right for DS1.
The kids were also remarkably uninterested in the outdoor thing they run, most I spoke to never went there!!
I personally thought that the day pupils seemed more together and in fairness all we spoke to observed seemed very happy and chilled perhaps many too chilled? Not sure that makes sense.
Just a thought as your obviously south/south west what about the a Royal High School at Bath my friends daughter joined for the 6th form, they take a large number of boarders into their 6th form 30+, and have a boarding house only for 6th formers nearly all started at the same time, she's been very happy there, the staff have been very caring, all the girls Ive met have been delightful, and she's a lovely girl and not a designer label clad, eye wateringly sophisticated streetwise individual just a genuinely nice girl they've really encouraged and supported her, boosted her confidence and she's done exceedingly well and from yesterday now knows she's off to UCL. Probably out of your area but do PM me if you want to know more.