Mom won't let me go out for NYE because of my bipolar

You don't need to drink to enjoy yourself. You don't need to have alcohol to make a celebration special. Like you said, you are 28 years old. Your mum can share and express her feelings, but that should never be the orders you follow. You are an adult and can make the decisions for yourself. And once you have proven to yourself you can, that will prove it to her too.

Maybe just limit yourself to 1 glass for the occasion. I personally don't drink but can always have a good time.

Move out

Well technically that could happen any day of the year. Maybe make the plans for before midnight. Not sure if getting home before the actual "ball drop" would comfort you and her. Or ask them if a movie night at your place would be good