Everything depends on the remarks on the experience certificate that your bank will issue to you after the dismissal. If the employment certificate is "neutral" then there is no need to worry as such. When the government employees are removed on disciplinary grounds, not necessarily the reasons for their dismissal are mentioned in the employment certificate unless the offence committed is grave or the offence that falls under the purview of "moral turpitude".
If you get the certificate with negative remarks then it will nullify your career in the bank. I say so because there is no point in showing this certificate to your prospective employers. If you show this type of certificate to your prospective employers, with the obvious reference to your questionable integrity, I am afraid that they will consider your candidature. In such case better not to mention about your employment in the bank and start applying as a fresher!
6th April 2019 From India, Bangalore