I presume this is the news story you are talking about, OP? www.bbc.co.uk/news/uk-england-bristol-37419986
I'm not local to Knowle, so don't know the issues with the current users of the likely building etc, but I do know BGS. I think you might be letting your prejudices affect your judgement when it comes to what you believe the attitude of parents would be: "The private school parents will not want their experience diluted by mixing with the hoards." Have you ever actually spoken to any of them? BGS has never been a 'posh' school like Clifton College, and I think most people send children there for its academic reputation, not for social exclusivity.
Until the 70s, it was a direct grant grammar school, so a fixed number of places (around one third?) were state funded for people who couldn't afford fees. Then when grammar schools were abolished, a large number of pupils still had their fees paid by the state assisted places scheme. I was there briefly in the 1980s and a lot of my friends came from working class families in areas like Stockwood and Bedminster, and their parents did not pay fees. Since the assisted places scheme was abolished, the school has tried to fill the gap with bursaries and scholarships, but obviously does not have the big endowment funds that old public schools have so cannot offer bursary places to everyone who would like/benefit from one. Even so, there are plenty of children there now from not-posh areas of Bristol and the outlying areas, and I would guess some of them have bursaries, but no one knows who has one and who hasn't. I certainly haven't heard of any us-and-them attitudes between full-fee-paying and subsidised students.
I don't know the ins and outs of the plan for the new school, but I would be extremely surprised if the underlying motivation was to get rid of bursaries at the main school, as some previous posts seem to suggest.