What do the abbreviations S.O., B.A., and B.O. stand for in Nancy Mitford's novel?

I’m reading a novel by Nancy Mitford, who writes about the WWII era British aristocracy; there is often a fair amount of slang very particular to that class and era. Usually I can figure it out by googling it, but I’m having a hard time with this one and there are no real context clues. It was used like this:

“What can be the matter with Polly? So beautiful, and no B.A. at all.”
“S.A.” said Lady Patricia faintly, “or B.O.”

It’s driving me crazy—can anyone help?