If you find evidence that he was in fact still married to his first spouse when you married, you may seek an annulment based upon the invalidity of your marriage. If you cannot substantiate your belief, or prefer to simply move forward without investing the time and energy in trying to find out if the first marriage was dissolved. you can simply file for divorce.
You can file a divorce where you live, but if your marital relationship was in Nevada your ex- can insist that issues of property division (if there is any property or debt to divide) occur in that state. Your having waited more than a decade to claim that he should contribute to old bills is likely to complicate any effort to divide that very old debt.

