I know next time for my personal development to not freeze up and shut that sort of thing down before anything really gets said.

This is really great and I'd personally work that into an apology to the person. I know you don't have a responsibility to police others thoughts, but everyone vents and you don't always know when it's not safe to do so. As a professional courtesy though, giving a simple heads up like "we can chat later, I'm with a parent right now hint hint wink wink" can save you both from getting in trouble.

Also next time "We were gossiping" not "She was gossiping". You already know that so I won't harp, but words matter. You can be a really nice person, but through your words still screw over your colleagues.