Thanks for the update. I think "psycho" is borderline, tending towards not-bigoted. Some words, like "nuts" and "crazy" are often used as synonyms for "irrational" or "unrealistic" or even "impressively unusual." Others, like "schizo" are "crippled," are usually not used to describe behaviors or situations. I've not heard a person use "crippled" as a descriptor for another person if they weren't referring to an injury or illness that resulted in mobility issues.
I guess what I'd wonder is whether or not you think she actually meant "psycho" to denote the diagnosed mental illness or she was using it (albeit insensitively) as a way of expressing that this person was behaving in an irrational and inappropriate way. In short, had she dropped the diagnosis, would you have thought she was using "psycho" as a pejorative term for someone with a diagnosed mental illness, or as a slang term for someone who was behaving in an exceptionally odd way?
To use another situation, suppose a different friend was describing her neighbor's teenager. Let's say that this kid liked to emulate a particular television show that features a group of men doing silly and often self-destructive stunts, and he landed himself in the hospital after jumping off the roof, attempting to leap over a speeding car, or letting one of his friends hit him in the head with a bottle. If the friend called the kid "moronic," would you think she was being bigoted? (Keep in mind that "moron" did at one time denote a particular IQ range.) Suppose she had mentioned that he had a mild learning disability. Would you assume that the "moronic" referred to his choices or his disability?
My point is that assuming that a person is a bigot is not particularly charitable, and because this particular term isn't widely recognized as a slur, it's entirely possible that she wasn't intending to be offensive or disparage an entire group of people. (Racial and sexual slurs are a different story, as they are pretty much always intended to demean.) In this instance, I would not have interrupted her tirade, but later on quietly let her know that her term offended you. Interrupting someone's rant to accuse them of bigotry isn't going to go over well, so if it isn't clearly intended as a slur (or bullying), I don't think it's worth stepping in.
FWIW, I have not heard many (if any) people use the word "psycho" to literally mean "psychotic/mentally ill." Most of them use it to mean "disturbingly erratic" or "inappropriately unpredictable." In general, the behaviors (and people who engage in them) I've heard describes as psycho involve a lack of restraint. They might not be able to express their emotions in a controlled manner. They might not recognize boundaries. The common factor is that they don't quite exercise the self-censorship that is socially expected.
I also agree that it's probably best to not hang out with this group any more. I don't think they are bad people for not taking this particular term as derogatory or bigoted, but if you are on different pages about it and it's very important to you, they're a bad match.