No, your ex-wife cannot stop you from filing bankruptcy. Because it sounds like the main issue driving you to bankruptcy is credit card debt, we will focus on that.

Credit card debt would be an unsecured debt, meaning there is no collateral pledged for the debt (as opposed to secured debts like mortgages or car loans). Unsecured credit card debt is dischargeable in a bankruptcy. When you are discharged from a debt it means you no longer have any obligation to pay on the debt.

Is there is a divorce judgment that says you have some obligation to pay on the credit card debts? Even if there was, this does not stop you from filing bankruptcy. If your ex-wife feels there is some reason why you should not be discharged from paying that debt, then it is up to her to hire an attorney and she will have to file an objection in bankruptcy court as to the dischargeability of the debts in question. The bankruptcy judge will then decide the matter. This, however, is not being in contempt of court. This is just a matter of whether the debt is dischargeable as to you.

After the bankruptcy,if it is a joint debt and you are discharged from being obligated to pay on it, then creditors can no longer pursue you on the debt. However, they could still pursue your ex-wife if it was a joint debt.