To each their own. With a friendship triad, we have a 'everything you tell me, the other one will eventually hear, too' agreement. I'm not a hugely private person and tend to stick to the rule 'if there is something I don't want someone to know, I won't tell it to anyone'. In practise I find it exhausting to try to remember what was okay to repeat and what wasn't, so I try to tell people not to share something with me that is truly off-bounds from being told to anyone else.
As to gossip, if it's one-way only, that's potentially an unhealthy sign for me. I mean, you and B keep on talking about the personal life details of A, but you never share any of B's stuff with A (this is a rhetorical question, I honestly got confused with the letters :P). That would border on gossip, for me.
Me: bi female in my twenties