OK. You're on your deathbed. Who's with you. Your wife? Your girlfriend? Just your family and friends? That will tell you what your heart wants. If you want to be married or just in a relationship, being bipolar won't interfere with that. If it will, and not because of what she thinks mind you, then yes you shouldn't be dating right now.
You're bipolar. That's not who you are, that's a part of you. I'm diabetic. That's one part of who I am. If she has problems with you being bipolar, especialy if she can't handle it, then she's not the woman you're supposed to be with. Because although she may or may not totally understand the illness what will matter to her is how it affects you. You plan to be there for her no matter what, right? Then why shouldn't she be there for you no matter what?
Who does your explaining you illness to seem insurmountable? You? That's an issue you really should deal with before you start dating. It wouldn't be fair to her otherwise. To her? Seems to me you're not giving her much credit, if any at all. If I were her I wouldn't date you either.
Here's a towel. Dry that bucket of cold water off your face.

Now go make some lucky woman very happy.