Answer by William Gets:
It seems logical that Google would down-list a page with a high bounce rate against a competitors page with the low bounce rate.
But apparently, a high bounce rate does not affect the position of your webpage on a search engine results page. I have often asked this same question with other SEO experts that I know.
A high bounce rate is therefore simply something that a website owner needs to fix because obviously people are coming to the page and then leaving straight afterwards. Better content on the page is usually the fix for high bounce rates.
However, in your case, it is logical for site B to have a high bounce rate so you have nothing to worry about.
And when you say “site B”, I assume you mean “page B”. Keep in mind, that a “website” does not rank overall on a SERP. It is the individual pages of the website that rank. So if you have one page that is not ranking high, the rest of your website pages should not be affected.