Sure, I think if you're motivated enough and have good grounding skills on top of a good medication regimen, you can do it. However, I can imagine a therapist job being very stressful if you're in the midst of an episode, so that's something to consider if you don't handle stress well. BUT stress is something we can learn to cope with, so it's not a road block.

That said, I don't think it's unethical to have bipolar and be a therapist. I wouldn't be surprised if some therapists have mental illnesses... because I can imagine their mental illnesses might be their motivator to help others.