Not a sufferer, but I have a friend who is and I have a strong understanding of stigma.
This person is not in work, but has been offered several jobs. They consider their bipolar a career asset. They are building towards a career in mental health education and advocacy.
Yes, you are in a different category to the rest of society, at least as far as society is concerned. Yes, people will make ridiculous and incorrect judgments based on the label. Welcome to the world of mental illness. Despite the fact that many, many people suffer from mental illness, people often still continue to hold the deluded belief that people with a history of mental ill-health are somehow 'different.' We all tend to make labels. Any groups of people that you dislike? One common one is fat people, who are discriminated against enormously under the guise of 'but they're unhealthy and it's their own choice' - which isn't the case much of the time. People discriminate. It's what they do. It's an unfortunate reality with strong roots in the evolution of the species. We form groups. We tend to be suspicious of 'out groups' - so people of one religion often are fearful/suspicious of those from different religions, people develop racism, or war with other tribes, or people who are 'different' in some way. Doesn't make it right and this sort of stigma is something I despise. Regardless of your mental illness, you're still just as human as the next person. You can fight this, or do what you can to mitigate the risk of discrimination.
Typically when considering work interviews, I would suggest you consider how much you want your future employer to know. Your health is none of their business unless it impacts on your intrinsic ability to undertake a role. Same as if you are married, or like a particular sport, or have a favourite colour - what's it go to do with whether you can do a job? In my country (Australia), you could have a case for fair work australia for unfair discrimination on the basis of disability. If you want to talk about health though, you could say, 'I had some health issues and have worked through these and am now more than work ready' or similar. You could tell the employer about your history of bipolar - yes, a lot of employers will judge you, but those who don't are probably going to be fantastic people to work for because they will have taken you as you are and didn't discriminate.