My advice would be to test his boundaries slowly before you let it all hang out. You don't need to let him in on all your emotional problems right away. I'm sure you have many great qualities/attributes and it's advisable to let him see those before he sees the emotional instability.
Some people are more equip than others to handle an emotionally unstable person. By testing him slowly, not only will you see if he is ready to handle your issues but you will have a chance to see if he is what YOU want and need.
First I would work really hard at learning your own moods, triggers, symptoms etc and recording all the strategies you have for keeping yourself stable. Get yourself well prepared for instability and how best you can keep yourself stable if you feel it. In the beginning of relationships there can be a lot of emotion, anxiety, anticipation etc, so you'll be able to manage any symptoms and see if there is a possibility for the relationship to progress further. If it is going well, it would then be time to see how you can include your new partner into your bipolar management plan.
I strongly recommend you get the book "Loving someone with Bipolar Disorder" by Julie Fast. I read it, even though I am the one with bipolar, and it gave me huge insight into what my husband has to go through and deal with, and as it was written by someone with bipolar as well as a doctor, it has tons of helpful, simple information that you can use by yourself, or together with a loved on.
Good luck and please do try and find someone special for a relationship. Being bipolar certainly shouldn't mean you can't have a full and happy life...healthy relationships included.
Go slow. Get to know each other. If you try to hard to impress or move the relationship along too quickly, you'll end up being deceptive. You don't want to be deceptive because at some point, the truth will tell. Trust God to bring the right someone along. He knows your heart's desire. Becoming impatient is a trap.