"Why Gay from China" as well. I mean it sounds like she spent time living in China, but she wasn't there at the time of coming to the Chalet School, and I never got the impression we were meant to picture her as Chinese.
Makes sense if her story is in a cross over book though, it always read like it was written somewhere.
The real strange naming (to me) is the Armada "Lavender Leigh at the Chalet School" when I first read it, I remember saying that the title should so obviously be "Lavender Laughs in the Chalet School" ("Lavender Laughs at the Chalet School" would have quite a different meaning
) It was only later I found out that was the original title, so why did Armada change it. 
I agree about Miss Bubb. She could have been written as a wonderful person coming in and taking up the slack discipline and getting wonderful results, with only slight tweaking. In fact what she says to Madge when Madge dismisses her does show her in a totally different light.
I felt the OTT punishment to Gay was more to do with her getting frustrated because her authority was being undermined by everyone else.
I'm sure I've come across other school stories (New House Mistress, I think is one by EBD) where you have a beloved head (or in this case House Mistress) leaving and the school being up in arms. New Mistress comes in and realises that the school is used to much less discipline, and tightens up causing the school to hate them until they realise (in EBD's case by her saving the life of the main person) how much better the new way is. That's really the Miss Bubb in a positive light.
Come to think of it, that's basically similar to when they join up with the other Chalet School. There's also a Gwendoline Courtney ("At School with the Stanthorpes"?) along those lines.
But the difference with Miss Bubb is firstly she's only engaged for a term or two, so she shouldn't be making huge changes. She comes pretty much straight in and does them, and I don't think some of the changes were her choice to make on her own. She's also got that the staff and children are still in a state of shock at the situation, so she should have been treading fairly lightly at first anyway. She goes in as though she is totally in charge, which, with Madge so close by, she needed to know that Madge was actually in authority over her.
When we got a new head after about 15-20 years at secondary. The old head, whereas wasn't a pushover, was much loved especially by the boarders. The new head was viewed very much with suspicion by us as pupils, and I suspect he did find us rather unwelcoming at times. However I don't recall any changes made in his first term (he arrived at Easter) other than he introduced a short talk after the reading in assembly. And actually we rather liked it because, with a really good long talk, we could miss half the first lesson. 
He made one or two (small, but we moaned about them at the beginning, although we grew to like them!) organisational changes at the start of the new academic year, but it was another year after that that he made changes that were bigger.
So it was 4 terms in before he really did any decrees that really effected things.