it depends, I'm diagnosed as bipolar - so I would like to be with someone who understands me, although if she was severely ill - I dont think it would be good for either of us. but i wouldn't judge until getting to know her.
It would be tough. Me, myself, I'm constantly worrying about pleasing people and making sure I'm not doing anything wrong so they can be happy. And if someone just turned randomly displeased with no explanation, my brain probably would always come round to the thought of me doing something wrong, and I feel the emotional disconnectivity might escalate from there.
Not saying it's not possible if you don't fight for it!
My mom has bipolar disorder, and at the moment, has it very well-controlled. She has not had any 'outbursts', or depression, in several years. If the hypothetical individual's bipolar disorder were mild/controlled, similarly to my mother's, I would absolutely embrace an opportunity to start a relationship with her.
Conversely, one with severe/uncontrolled bipolar would likely be too difficult for me to handle. I require a good level of stability, and reliability in a partner; both of which directly contradict the idea of an uncontrolled, severe bipolar disorder.
As already noted by @MAP I would be unphased by the possibility, although a greater need for self awareness and medication checking would be necessary, more so knowing I don't always relate to severe manic phases in anyone and can find the residual recklessness that goes with the pleasure seeking state very daunting.
For example one of my closest female friends has bipolar and I find it easy to separate bipolar thinking patterns from her true nature, of being very warm, loving, extremely honest and a good listener (well she does have her hurdles when it comes to full employment but she accepts me so I accept her complexity too).
For me it would depend on one major factor. The person who is diagnosed, does he/she accept the diagnosis and has learned or is willing to learn to live with it?
I have two cases wich lead me in this.
The first one is a woman who has been diagnosed with bipolar. But has accepted this and is learning to cope with it. Through medication and therapy.
The 2nd one is diagnosed with it, but has not accepted it. Neither therapy or medication.
The 1st I could pursue a relationship with.
The 2nd one I couldn't. I've seen what happens when a person doesn't accept it. It's not pretty. Not for them, and not for their partner.
If the person was properly diagnosed and treated and compliant with treatment, then I would be fine with that.
If the person was not properly diagnosed and treated, or if there was a lack of compliance with treatment, then definitely not. I had close contact as a child with someone with untreated bipolar and an addiction and there's just too much pain that comes from that situation. It's hard, though, knowing that person probably wants and needs to be loved, but the manifestation of the behaviours related to the disorder are too difficult (and sometimses abusiv) and, really, diagnosis, treatment, compliance with treatment . . . those are, generally, choices, so when this person I do know with bipolar makes the choice to not be treated, I feel like they're basically choosing the disorder over me, and I can't be in any sort of relationship with that person.
That said, I may also possibly have bipolar (speculated; not currently diagnosed); the last time I needed psychiatric treatment, the course they pursued was one that would be used for bipolar and I was stunned by the effectiveness of treatment in comparison to previous efforts to treat depression. If treatment for bipolar is what brings me to a place where I feel well, then that's amazing and I want that.
I wouldn't have a problem pursuing a relationship with someone who has bipolar disorder as long as she's working to control it. Of course, I have bipolar disorder myself, so I'm probably more understanding of it than the average person. It would also be nice having someone who understands me, but there would also be the risk of having two volatile personalities together. Then again, my mom and I (both diagnosed as bipolar and taking medication) usually get along just fine.
Possibly the biggest reason I can personally think of for not pursuing a relationship with a bipolar person is that I'm the type of person who intends for any relationship to turn into marriage and a family. Since bipolar disorder is highly genetic, I'd worry about passing it onto any children. There's some risk with one bipolar parents, but a whole lot more with two.