I worked at a credit union 3 years ago and the agency that bonded me for them said I was not able to be bonded by them anymore after bouncing some checks. That credit union closed and I left. Now I am applying for a job at a bank, will I be able to be bonded again? This is in New York state.

You can only try, we don't know what you have done in the interim and a police check does that.

All you can do is try, it will depend on the bonding company, the rate the employer is willing to pay for the bond, and the level of risk the company has set up as acceptable.