never lie in a job application - you will be found out, and it will end badly. also it will not help if you need references in future.

as for being able to teach while bipolar - i don't know, i guess it's just something to find out. i've managed to get around this in job apps (not for teaching, but for fairly stressful customer based work) by admitting that i have had to leave a couple of jobs through illness - if they ask further what the illness is, i say it's bipolar but it's controlled etc. if they have a problem they can ask further questions to ascertain your suitability - but if you have been honest - they will be too. there's no need to go into detail unless you are pushed, but don't hide things that may be important, and don't lie. but that doesn't necessarily mean you have to tell the whole truth - you don't need to give gory details of everything, just explain the situation in basic terms and move on.

good luck!!!