What are the career opportunities abroad after being employed for a few years?

If you want a job in some foreign country then you have to keep a thorough watch on the job portals and shortlist the jobs of your choice matching with your qualifications and apply for them. If you get an offer then your employer will sponsor you and there will not be any problem for you to go to that country and get a job Visa for working there.
When you go through the job portals then you would find some positions where you might be interested but your qualifications would not be suiting properly for those jobs so in such a case you can decide to go for some short online course in banking and finance areas. I would recommend sites like Coursera, Unacademy, Udemy, FutureLearn, Udacity, Skillshare etc for acquiring such qualifications.
MBA is a very general qualification today but the MBA in Finance might help you in seeking a job in foreign countries. There are good positions in insurance and risk management areas also and you can consider that also an area where you can think of acquiring some short course.
Please note that there is a good rush of candidates for foreign positions in many areas and banking is one of them. It is obvious that there would be tough competition when you apply for a foreign position and you have to acquire necessary skills which give you advantage over other candidates.
Another thing that could help in the matter is try for some niche course in some foreign University after which you can try a job there itself. Only thing is you may have to leave the present job if you get admission in a good course abroad.

The best option for you would be to understand the different working areas of the bank and ensure that you are familiar with all such working operations employed in your bank. At the same time, you should have good rapport with your topmost officials so that you are ranked as an efficient executive in your present assignments. Continue your job in the existing assignments for at least two years after your probation period. Then you may ask for a favour for a transfer to some SBI bank existing in the foreign country of your choice. This would help you to understand the working situation of that branch.
Now residing over there for at least three years, you can continue your studies in MBA in finance on part time basis to understand the different tools of finance such as Finance and Risk Management, Profitable Investment of Resources in the different industries etc.
Understand the different procedures of banks working in such a foreign country and move to a foreign bank with your interview for such a bank.
Following such strategies, you could have great openings in the foreign banks.

With graduation and some experience in SBI, it is difficult to get a chance in foreign countries. They look for candidates with higher qualifications. You can try any one of the options mentioned below.
1. There are many job portals like Naukri. com. You register yourselves in that portal and place your resume there. You will be getting alerts from the portal about various jobs that are suitable for you. At the same time, you can search in the portal for any foreign jobs and you can apply for them.
2. Meanwhile, try to improve your qualification. I suggest you go for bank-related software courses more than MBA. These skill-based courses will give you a better chance to get a job there. There are many certification courses like tally, ERP and some other courses. You can try these certificates. That will increase your chance of getting a job abroad.
3. The Association of Chartered Certified Accountants (ACCA) is a global accounting body. This is having more than 2 lakh members and 5 lakh students. The ACCA course online will teach skills required for your job and also good skills but learn about organisational management. This certification will give you better chances to get a job across the world.
4. SBI is having branches in foreign countries also. You can try to get a transfer to one of those overseas and after going there you can try for a job there and make a shift.

You need to develop more skills before seeking any job in foreign countries. As told by you that you are only a graduate and have some banking experience. I think It would not be sufficient for getting a job in foreign countries. At first, you should apply your resume on job portal and when any job matches your qualification then they will send an alert to you. But before that, you should take the banking-related certificate and diploma course. This course would make strong your resume and help in find job in foreign countries. Another way is to go to foreign countries through transfer. There are branches of SBI in foreign countries. You try to take transfer and residing there you can try for another job.

It depends on what graduation you did before working for SBI. So based on it there are lot of options for Post graduation Masters program. Now question is for MBA , yes it is absolute choice if nothing works but in order to secure good university you have get good score in GMAT. Also GMAT score is considered many countries line USA , Australia. Plus you will have to pay their fees which would be in lacks depends on subjects you choose. Some universities offer scholarships from 2nd semester/ trimester onwards.
So if you really want to settle down abroad start preparing now. All the best.