I was in the same situation last year. I ended up completely dropping Bath because even though it was the uni I liked the most visiting the city was too small/dead for me to consider living there. I worked for a year before starting, but the poshness of people is the single thing I'm most worried about in terms of settling in. It really varies by accommodation though - UH, which I'm applying for, is the lowest at about 20% private schooled, though that's still about the same as the majority of other Russell Group unis and about three times the national average.