I don't expect a woman to share that information on a first date. Probably not even on a second, third, or fourth date. But by the time it goes from casual dating to a serious relationship, when we've established trust and comfort with sharing the deeper levels of who we are, I feel it's something I should be aware of. If she wasn't bisexual at the time but, rather, slowly discovered her attraction to other women during our time together, I'd hope she'd share those feelings with me. At the very least, she should tell me as soon as she came to terms with it. Because if she kept it a secret from me, it'd force me to call into question why she didn't tell me and what that says about our relationship that she didn't feel she could share that part of her with me. If I broke up with her, it wouldn't be because she was bisexual, but that she didn't trust me enough to tell me or kept it secret for reasons beyond my comprehension.
That said, I wouldn't date/would break up with a bisexual woman who expected her bisexuality to give her a free pass for fooling around with other women because, in some twisted logic, that wouldn't be cheating. Or if her newly discovered bisexuality, or bi-curiosity, compelled her to explore it, if she felt she needed that experience, then I'd have to end the relationship. But if she's fully committed to me and our relationship, if she's attracted to other women (along with other men) but doesn't feel the interest or the impulse to pursue other lovers so long as she's with me, I'd have no issue with dating someone who's bisexual.