If you don’t ever want to talk to him again, why do you care what he thinks of you?
Okay, I mean I do empathise…sometimes it even bothers me when strangers on the internet assign untrue causes to my behaviour! But really, it shouldn’t, and I think you’ll feel better if you’re able to brush him and his whole deal off. Don’t invest any more time or energy into something you don’t respect or appreciate.
I can see this becoming a problem if he starts trash-talking you to mutual friends. But with a little effort you can easily set them straight. Just act nonchalant whenever his name comes up: if you don’t exhibit any emotions for him (negative or positive), no one will think you have any, no matter what he says. If anyone asks you about what he says about you, just brush it off in a somewhat condescending tone: “Oh as if, I’m not emotionally-scarred, I just wanted out of that train wreck. Later for that shit!” and then casually move on to a topic you find more interesting.
If you want to try one last time to explain yourself to him, be clear, direct, brief, and unemotional. Steel yourself before you see him and keep it up (don’t be so cold that you seem upset—take more of a bored tone). No matter what he does, don’t let yourself get worked up because he’ll just take that as proof that he’s right. (And he may try and work you up for that very reason so be on guard.) I’d say something like “Listen, you fucked up and you acted like an ass, and I don’t think you’re evil but I’m just not interested in putting in the time or energy to work things out with you. I don’t respect you, I don’t like you, why would I want you around at all? You can tell yourself that I’m dramatic and emotional all you like, I really don’t care what you think. Good-bye.” You may not want to be that harsh but you should be that straightforward.
But frankly, I don’t think it’s worth the effort. I think the reason he wants to be friends, and the reason he’s calling you over-dramatic and emotional for not wanting to be friends, is because of how it makes him look. I mean, everyone knows that most relationships don’t last forever, so the fact you two broke up isn’t telling of anything. But if two people want to be friends after breaking up that means the split wasn’t a personal indictment of the other: they still respect each other and like each other, they still believe the other is a good person and they want that person in their life. But if you don’t want to be this guy’s friend, that’s an indictment of him, a public sign of disrespect. He doesn’t want to acknowledge that he caused the split: he wants to think of it as natural and mutual. He doesn’t want to admit he made a mistake. And it’s a lot easier to think of the split as natural and impersonal if you and he become friends. You don’t want to be his friend, so now he either has to face-up to why that is, or come up with another reason. He’s not gonna want to let go of that reason, it makes him look good after all, so the more you engage with him about this, the only thing you accomplish is stretching it out and, really, proving his position that you are emotionally involved.
Whatever you do, good luck!
By the way, I think it’s a stretch to say you think he’s bipolar. I mean, I’m not comfortable with medical words being thrown around like that, I think medical diagnoses should be left to medical professionals. And really, what difference does it make, why he acted how he acted? For you it comes down to the how, right, and that is why you don’t want to be with him? So, I think it’s better for everyone (you, him, your readers) if you stick to what matters and what you know.