From what you've written, it seems that you and your girlfriend are fundamentally incompatible. If a poly or open relationship is essential to her, then that is a deal breaker. You two don't want the same style of relationship and this is usually not something that can be finessed around. And it sounds like poly would not just be uncomfortable for you but actually damaging. I wish I had a better assessment for you.
And now for the unsolicited advice.
Please reconsider not using medication to treat your bipolar disorder. My ex has bipolar. It's been her experience, backed up by various studies, that people who do not treat bipolar with medication, or they go on and off medication, are much more likely to screw up their lives - career, relationships, health. Or they just don't survive. The disease kills them indirectly through health issues causes by the harsh toll bipolar takes on the body, not just the mind, or through addictions or thrill seeking behavior, or directly through suicide. Yes, the medications often have absolutely vicious side effects. My ex hated the ones that clouded her thinking (she's a scientist.) But there is a broader range of medications available. There is a combination out there that will not cloud your artistic expression while treating the disease. Please think about it. Your sanity and continued survival may be at risk.