How do I handle my boyfriends bipolarness without feeling like I'm always walking on eggshells?

Wow. Your bf's bipolar disorder needs to be managed by his doctors. You may wish to ask your bf if you could speak with his treating physician/psychologist to get ideas and tactics to help deal with his problem at your level of interaction. Visit the balanced mind foundation website to get pointers on bipolar disorder.
Talk. Tell him how you feel, and focus on yourself and your feelings or he may become defensive or just shut down. You may feel rejected or unwanted, or even scared. Communicaton is important to any relationship. Ask him if everything is ok. Keep an open line of communication during good and bad times.