Advice about whether or not to tell other people you have bipolar disorder runs from one extreme to the other. People who have had positive experiences say, "Go for it." People who have had terrible experiences say, "Never tell anyone" Is there a happy medium?
Actually, I don't think there is. Just as every person with bipolar disorder is different, every situation is different, too.
Take me. I have never had a single person treat me badly, draw away from me, or drop me because I said I had this illness. I'm very frank about it, partly because when people ask me what I do, I say, "I write on the internet about bipolar disorder." The funny thing is that when I do this, nine times out of ten the person says, "Oh, my [spouse, ex, sibling, parent, friend, etc.] has that," and we get to talking about it.
But - I am self-employed, working from home. Before that, I worked at a very small company (about 10 employees), and at work the routine and structure made my symptoms (mostly depressive) manageable. My best friend worked there, too, and could help me through things. And no one who heard me talking about my bipolar disorder seemed to care much as long as I did my work.
Before I was diagnosed, when I worked at a large company, I had problems with bosses at work, but that was because of behavior issues, not because they knew I had a mental illness.
So my situation has put me in a position to be open. If someone does freak out, which hasn't happened yet, it's that person's problem, not mine, and by talking calmly and rationally about the illness, who knows, I might be able to turn the situation around.
I've been lucky, I guess. Someone with poorly controlled symptoms, an unfeeling supervisor, or a church that believes prayer alone can "cure" mental illnesses, etc., probably wouldn't be. Sometimes someone you trust wholeheartedly will react badly in a way you couldn't have imagined.
As you can see, I'm not going to give any advice except this: If you can do your job but need "reasonable accommodations," look seriously into your rights under the Americans with Disabilities Act. Bipolar disorder is covered under the ADA. Most employers are required to make those reasonable accommodations - as long as they don't cause the company undue hardship. This will require you to tell your superiors that you have a mental illness, but it might still be in your best interests to do it. Only you can decide.