Should I tell my parents that I am bipolar?

My parents and I don’t have the best relationship (they were abusive when I was younger, but stopped when I got older), but it’s definitely better than before. They know that I’ve had suicidal ideation in the past and depressive symptoms, and they didn’t take it well at first, but as years passed they’ve come to terms with it, and tried to show concern for me sometimes.

Recently they found out I’ve been secretly going to a psychiatrist, and they didn’t say anything about it or ask me about it either. I want to just give them a heads up that I have bipolar, I want to ask them to go to the psychiatrist with me just once to understand what I’m going thru, but I’m not sure how they’d react this time. They already know that something is up with me, so I don’t know if the extra clarification will be meaningful, and my therapist says that I don’t owe them an explanation, but I feel like I want to be more honest with them.

Should I tell them I’m bipolar?