I'm diagnosed Bipolar I (the classic manifestation), and he is diagnosed AS. It would be difficult to say either one of us are typical in those categories because everyone is their own individual. I've never had an issue getting dates, and probably the real difficulty has been making the guy understand any ups or downs are not his fault. Most generally I am a little offbeat, but fairly level-headed. After my diagnosis about seven or so years ago, I became more away of the bipolar label. While I was happy to have a diagnosis, and have treatment options--the sheer stereotypes have prevented me from talking about it much. I don't care to be judged primarily on a diagnosis. Not to mention, there are a lot of people that like to say "so and so is/ must be bipolar," when it reality it just seems that person is a simply a jerk with more than likely some other issue going on. Just my perspective. I am more than happy to discuss it with people when I feel it can be helpful for them, and there are good things that do come from educating people if possible.
With my mixed relationship, there have been misunderstandings on both of our ends. I explain it as the person that has went through every emotion there is, sometimes on a weekly basis (me), dating a man who is no less emotional really--just has problems processing them. It makes for an interesting mix at times. I have found it has been beneficial for each of us; there is some weird understanding. Also, I have noticed some overlap between us. As social as I CAN be, he seems to enjoy that, the getting out and about. However, it leaves me emotionally exhausted (him as well), so then we can be introverts together. If I am down, of course he gets worried, but understands because he gets down in his own way sometimes as well. I have not had full mania for quite some time, but still get hypomania every now and again. So after I've spent several days consumed by some seemingly inane task, or deciding I'm going to re-arrange the entire house at one in the morning, it would be horribly misunderstanding of me to criticize his current interest, and the single-mindedness it brings. I take his words seriously if my behavior becomes unhealthy, and he seems to reciprocate that sentiment about any concerns I have with his.
Anyway, that is a (so far) positive story. Unfortunately, it is probably not the norm. Personality types are so varied, and a diagnosis of anything cannot predict chemistry or what type of person someone is. I don't feel broken. Maybe frustrated is a better description. It is hard to be at the mercy of whatever emotion might be lurking around the corner. I think for you to request a bipolar girl would lead to some interesting responses, but probably not the kind you would like. I can't speak for any other female bipolar, but would be suspicious if I ran across an ad like that. You would be better off writing a dynamic, and honest, piece about yourself. Quirky comes in all varieties Best of luck!