Bipolar & teaching

Hey! Legally they can't discriminate against you, but in practice there are bigots hiding everywhere. Legally you have the right to not declare that you've got bipolar, though on insurance forms it's different. If it is for insurance purposes, you have the right to arrange it directly with the insurer without the school seeing the details. I'd do that for health insurance and disclose everything, otherwise they could use that as a way to disqualify when you come to claim, even if it's completely unrelated to your meantal health.
Based on what you said I'd advise you use your judgement about whether to disclose. Does this school have a reputation toward being conservative/ is in a conservative neighbourhood? If so it might be best to leave it off the form especially if it hasn't been a problem.
I have bipolar and work as a tutor, which is a bit different, but I don't disclose it because I know how to manage it. Best to avoid the stereotypes where possible.