Gayle King says she wasn't expecting a public apology from her ex-husband after dredging up the time he cheated on her during an interview ... but it means a lot to her that he said he was sorry.

We caught up with the famous TV anchor in New York City Thursday ... and we had to ask about her ex William Bumpus' mea culpa.

Gayle says, first off, she's shocked Bumpus talked to us ... he's a notoriously private person, and she was surprised to read what he told us about the whole incident from back in the day.

She then adds the public apology was super meaningful to her ... and the reaction from other women in the unfortunate "I've been cheated on" club has meant a lot to her too.

ICYMI ... Bumpus offered another apology to Gayle, their children Kirby and Virgil, and their families for the pain he caused several decades ago when Gayle walked in on him cheating on her with someone she considered to be a close friend.

Bumpus says Gayle has every right to tell her story ... and he notes they have a good relationship these days -- something Gayle backed up during our conversation with her Thursday.

In fact, Bumpus said King recently reached out to wish his teenage daughter, Poet, a happy 16th birthday ... the kind of classy move we've come to expect from Gayle.