I think it has a lot to do with the friend and how well you know them. I wouldn't, for example, just blurt "Hey! Did you know I am bi?"

The basic guidelines I follow are:

I act like myself. I comment on guys and girls and look at guys and girls. I don't hide it (mostly) but I don't flaunt it either. I am mostly modest to start with and that extends into this aspect of my life as well.

If it isn't brought up in topic, then I leave it alone. I don't toss it in a conversation like:
"Hey you want a cup of milk?"
"Yes, sure, and I'm bi, thanks."

There really isn't a need for that :)

If the topic of sexuality comes up or some other similar topic, then I mention it. If they seem uncomfortable, then I explain that it's like being straight. I explain how they are friends with the opposite sex without being romantically involved and I am the same way. Just because I can fall in love with both sexes, doesn't mean that I want to jump on it at every moment with every person I see. I am bisexual, not a nymphomaniac.

Then I say something like "if there is anything about it that bothers you, feel free to ask questions and say what you're feeling. I'll answer questions and listen to your concerns. I won't hold it against you." I am pretty open minded. This usually helps a lot with easing fears and concerns.

There is no exact time to say that. If you trust that your friend is really close to you, tell him/her now.

This is kind of funny because when I was in Grad School in the 1980's, I had a group of about a dozen or so relatively close friends. Some were gay, some Bi, some straight, several just downright confused, and some that didn't seem to have a permanent preference, it just depended on how they felt at the time. God there were some goofy days (and nights). The conversations we had... "so hey, are you into guys tonight?"

But back to your question. I would say that a couple of inappropriate situations might be while you are in the hot tub together, or in a gym shower-room after a workout. Then again, the hot tub might turn out to be the perfect time for it. Appropriate times might be when ever it comes up in normal conversation.

I don't think it's so much WHEN you bring it up. What's important is HOW the conversation goes. OK, you're bisexual. Does that mean you are attracted to women the same way you are to men, do you have long term relationships with either, or do you just like to have sex with one, and sex plus relationships with the other? Are you now or have you ever been attracted to your friend? If not, what will you do if you are in the future (correct answer: you will talk about it). I know that whenever I've had a gay friend who had a crush on me or just wanted to jump me, I preferred that he told me. We could talk about it and decide where to go from there.

If you are both able to carry on mature conversations about sexual orientations and relationships, I don't think it has to be too difficult. Might help to have a drink (or something), for nerves.