Be in the lookout for the advertisements from various banks for officers as well as clerical staff. For both graduation is enough. Apply for the posts and try your best. I think once you put your mind on the target and work hard you will be successful and you will have fair chances of getting a bank job.
If you want to pursue higher education go for MCA or MBA in a reputed institute. Then only you will be having the advantage. Otherwise, I don't think you will have any advantage of MBA or MCA in getting a job.
This is a very specific query for the career making and I will suggest you to go to Ask Expert section in this site where you will get many similar questions raised by the students and their detailed answers by our experts. Please visit that section. It is worth an attempt there to find the pin pointed answer to your problem.
What I can suggest in brief is that you prepare wholeheartedly for the IBPS (Institute of Banking Personnel Selection) exam. This is the exam held every year by IBPS for recruitment of banking personnels. Please note that there is a good rush for this apex exam in our country but if you prepare with hard work and focussed approach you will get through. This exam is held in stages and you can get the earlier year papers from this site or other internet sites for your reference. In market, guidebooks are also available. You can even join a good coaching centre also.
Knowledge is power.