I am not sure where you are based, but in the UK there is Government guidance surrounding the fitness of teachers. Bipolar is not an obstable to teaching as long as the condition is stable, but I do think you would have a responsibility to tell your employer if your condition is unstable and has the potential to impact on your work, the same as anyone else with a chronic condition (for example epilepsy, type 1 diabetes), particularly when you may have sole responsibilty for a a young age group.

Also in the UK there is the Equality Act which means an employer cannot discriminate against someone because of their health problem. I am not naive to think that smaller organisations do not look for the "healthiest" employee, but I do know larger organisations would be prosecuted if they were in breach of the legislation.

The benefits to sharing a health condition with an employer are that your employer could then be aware of any specific triggers that may impact on a health condition and ensure that there was sufficient support in place.

If a health condition was unstable and this was witheld from an employer, in this country that could lead to dismissal, not because of the health condition, but because the employee failed to be honest with their employer.

I know this is a difficult situation and I myself feel vulnerable within my own employment as no-one knows about my mental health struggles, but I think it is important that we do take responsibility for our ability to undertake our role, particularly if it is essential that we are able to make sound, rational decisions on behalf of others.