Will having a hysterectomy effect bipolar disorder?

No: Having the uterus removed will not affect psychiatric disorders. The stress of having surgery might be a factor though.

It possibly could: A hysterectomy can be traumatic in some cases, especially for women still in their child bearing years or may not have completed their family. Cancer of the uterus obviously is more than stressful in that situation. The younger the woman the more likely hysterectomy will cause stress. Bipolar disorder symptoms can easily occur under such stress. Honestly any hysterectomy is stressful.

Bipolar: Agree with my colleagues but add that another possible influence would be hormones.