Abuse causes mental, emotional and physical stress. If you face the abuse related stress for long periods of time you can develop borderline personality issues and post traumatic stress as well as all manner of physical health problems.

The prolonged stress can burn you out and leave you in a depressed state. If you have a history of depression or bipolar, than the depression caused by unmitigated stress could trigger a cycle.

I think regardless of whether or not you have a family history of bipolar, abuse is going to destabilize you sooner or later. If you have a history of family mental health problems, then more than likely you have a higher risk profile for going into a manic or depressive phase.

Ultimately, I think it is the prolonged stress reactions from abuse that causes imbalances in the body that can make you more vulnerable to BP but abuse in and of itself is probably not so much a contributory factor.

My experience with this comes from being severely abused by mentally ill parents for many years.

I hope that helps.