I wouldn't tell anyone unless you feel super comfortable with them and feel like they already like and care about you. When you first start dating, you'll only spend a few hours with someone at first, so hopefully you won't cycle too much in that time...and they can get to know you. Take things slow with people and see how they develop.

I dated a lot before I met my husband - I didn't tell people right away....I did it on a "need to know" basis. So if the relationship started getting serious....if sleepovers were becoming involved and they were going to see me taking medications or if they started hearing me having a lot of "dr appointments" which is my euphemism for therapy/pdoc.
I wanted to make sure people really knew me and liked me before i told them anything that would potentially scare them off.
Of the more serious relationships I had, nobody seemed to have an issue with it. Luckily everyone seemed to know someone or have a family member with some kind of mental illness so it made it a little easier.

My husband was probably the toughest one of everyone - I think it kind of went in one ear and out the other at first....when he had to deal with one of my episodes I think he may have wished he'd paid more attention when he realized it but he's very supportive now.

Dating is hard enough as it is...start with just getting into it before you get all caught up in full disclosure.