That sounds familiar...
It is difficult to just put oneself out there with MH issues on top of natural shyness and even scarier to tell them. It is not helpful, but my answer is just approach them but make sure you are as calm as possible so your nerves don't scare them off.
My opinion is to wait a few dates at the minimum to tell them, although depending on how you present yourself they may guess but they could write it off as shyness. At least wait until you know you like that person and feel comfortable. If you aren't all that into them, why broach the subject at all? If they like you enough for multiple dates, telling them should go well since they are getting used to you and they obviously like you.
Of course, that doesn't guarantee they won't end it. The stigma is real but don't let it stop you from trying. Waiting too long to tell them could be as damaging to your relationship as telling too soon as it could be interpreted at dishonest.
In short, it is a crap shoot so do what you can to improve your odds by helping them feel comfortable with you.
For friends, it is not as important to tell them in my opinion. I could be wrong.
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MDD with Psychotic Features, Dysthymia, GAD, Cluster C personality traits - Not taking any meds