I'm not going to tell my ex that I slept with someone she hates.
Why won't you tell her?
She is a mean person and a bad friend.
It's fine to keep somethings private. You're not together anymore, so who you sleep with is not her business. If she is mean and toxic, you should talk to her about her bad behavior, or stop being her friend.
You're right. Maybe I should stop being friends with her.
It sounds like you don't enjoy being friends with her if you describe her as mean and a bad friend. Sometimes it's best to just end friendships instead of trying to keep them afloat. There's nothing wrong with ending a friendship if you're unhappy with it.