I had a teacher in high school who referred to him as JB. My friend, the daughter of a close talmid of R Soloveitchik, was horrified. I don’t know where the term originated, but it’s currently only used by the yeshivish/chassidish community- Modern Orthodox people say “the Rav.” Especially in these communities, which have so much respect for rabbinic authority, I personally don’t see how people don’t consider how disrespectful it is to call a rabbi solely by his initials. (In writing, people might write RJBS or RYDS in the same way that they’d write RMF for R Moshe Feinstein- but that retains reference to the respectful title and is merely writing shorthand. Just JB is beyond that.)
One MO person once told me that she felt offended even when people would say R JB Soloveitchik- because she felt that yeshivish/chassidish people calling him by an English name is specifically looking down on him, because many consider it an inferior way of being called and they could refer to him (as plenty do) by his Hebrew/Yiddish name. I told her that people weren’t thinking about it like that and were’t actually being insulting, but I hope that in fact she is wrong about that (the indication on this thread is that it is just retaining the way that he referred to himself, which is obviously fine). But just saying JB is disrespectful.