In my experience, it should be on a need to know basis. You should probably clue in your family so that they can offer their support should you be in crisis. If that's not an option then a trusted friend perhaps. If you have a good, understanding boss at work then you could consider telling him so that he can give you time off when you're sick.
As for everyone else, the less they know the better. Mental health is a very personal issue and still widely misunderstood by the majority of people. Even though many people with bipolar disorder go on to live fairly normal lives, holding down jobs and starting families, we are still treated like whackjobs. I do believe its important to start a conversation to counter against this but not at the expense of your own wellbeing. Tell the wrong person and you will find yourself being met with criticism and judgement rather than support and no doubt rumours and misinformation will spread like wildfire. If you absolutely feel as though you need to talk to someone in the heat of the moment perhaps consider telling them you suffer from anxiety or depression, i.e. a more "socially acceptable" form of mental illness.
If you get to a point in your life when you feel secure in your abilities to cope, have a stable job and a loving support circle then yes by all means start that conversation. For now, keep your support circle small and be weary of who you trust.