I guess here's how I look at it, speaking as a transgender woman.

I'm pretty open about being trans. I'm comfortable with my identity, but if somebody came up to me and told me they knew I was trans, it would feel pretty insulting to me, because it means they can probably tell I used to be male. I would prefer to leave it up to my discretion whether to disclose my status or not.

With others, there is a wide range of feelings on this, so to play it safe, I wait for others to come out to me. If you want to encourage your friend to tell you about being bipolar, you could talk about your own experience with it. That might help your friend to feel safer about talking with you.