Hi N. Luis,
First of all, it took you 8 years to graduate -- which is a long time, but you have publications to show for it. I don't believe a hiring PI would care all that much about this fact, and you can simply call it difficulty with your project.
Second of all, chances are good that a future hire will contact your previous advisor, so be prepared for this. We have previous articles and forum posts about dealing with a negative reference.
I know someone personally who is on the bipolar spectrum. I recommend not disclosing anything while searching for a job, and even after accepting the job offer. I'll explain.
In the US it is illegal to discriminate against people with mental health disabilities. As of 2008, bipolar disorder is considered a "protected class" of disability and falls into this category. By law, you are not required to disclose your illness to your employer unless you need an accommodation; any kind of fallout from disclosure would also be discrimination and is illegal. (If you accommodation causes undue burden on your employer there may be issues, but you have said you are stable so I assume this won't be the case.)
Further, mental health issues are complicated and difficult to explain effectively. I believe the vast majority of people do not know the details of bipolar (starting with its name being confused for schizophrenia). With the law on your side, I see no reason to bring it up in the future.
Finally, the person I know with bipolar had great success talking about career issues with their doctor and therapist, who had practical suggestions for dealing with the job hunt. I was initially surprised that a psychiatrist would be so able to help, but I shouldn't have been: the doctor has seen hundreds of patients and had a lifetime of advice to give.
Best of luck, and please let me know if I can help further.
"The single factor that differentiates Nobel laureates from other scientists is training with another Nobel laureate." -- Sol Snyder