I want to go in the banking sector. I am pursuing B.Ed in regular mode. Also, I want to do MBA in regular mode at the same time. Is it fine?

MBA in regular mode along with B.Ed is not possible as both are full-time courses. I would advise you to concentrate on your B.Ed and post its completion enroll your self for MBA in marketing/finance/HR and then explore for an opportunity in banking sector in sales/service/training