Dear Hobe Sound, Florida:
I agree with you -- the Americans with Disabilities Act (ADA) applies to individuals who are disables, or individuals that are perceived to be disabled. It's obvious that you're familiar with the ADA, but here is a link so you have it with this discussion: http://www.ada.gov/.
Although you don't have bipolar disorder, at least three people think you do. Bipolar disorder is a mental illness, and mental illnesses can be protected under the Americans with Disabilities Act (ADA). Here's some information on how bipolar disorder can be accommodated under the ADA: http://bipolar.about.com/od/ada/The_Americans_with_Disabilities_Act_ADA.htm So, even if your employer wrongfully believed that you are bipolar, there are duties to accommodate.
The Equal Employment Opportunity Commission (EEOC) takes and investigates complaints of failure to accommodate an employee under the ADA. Although you've already been through the EEOC on an unrelated matter, here's a link to the complaint information for you: http://www.eeoc.gov/charge/overview_charge_filing.html
It's impossible to know if your employer is actually discriminating against you on the basis of the perceived disability without knowing the USPS side of the story, of course. Hopefully, the EEOC will be able to straighten that out for you.
With respect to her statement that you have a serious mental illness (bipolar disorder is considered a serious mental illness) that is defamation. Specifically, it's slander because it was spoken. However, since it was said in the context of an arbitration, it probably would be considered protected by "litigation privilege" ("litigation privilege" does not just apply to lawsuits; it also applies to other proceedings, including arbitration). If it was repeated outside the arbitration, however, it wouldn't be a protected communication.
Finally, I'm sure you already realize this, but because you are in a Union, you do need to work within the grievance procedures of the union first. However, you only have 180 days from the date of the discrimination to file a complaint within EEOC, so don't forget to do so.
Good luck with your situation.