It depends on the person. There are people I've been friendly with at work for three summers (seasonal job) and I've never told them. There are also people I've talked to four times and they know. It depends on the person and how trustworthy they seem.
I've also found when disclosing a mental illness it's important to be confident and straightforward so as to not make things seem awkward. If you can't do that, then maybe that's a sign you shouldn't tell that person.