Does my cousin have bipolar disorder if she's been married and divorced 4 times?

It's Possible. In and of itself, divorce does not automatically mean that someone has bipolar disorder. However, characteristics of bipolar disorder include impulsivity and risk-taking behaviors, including poor decisions in relationships. So, in someone who has been divorced 4 times, the possibility of bipolar disorder should be considered. Obviously, this diagnosis would require other symptoms as well.
No. Divorce is not a symptom of bipolar disorder. But if she married and divorced the same person, I would be suspicious that one of them had bipolar.