You have not mentioned your age. You have a B.A, English with 55%
1.Bank exams or IBPS exams are highly competitive, number of candidates writing this run in lakhs for a few thousand seats.The age limit is 21-28 years with a relaxation of the upper limit for SC/ST/OBC in the range of 3-5 years.
2.One of the basic criteria is a valid degree of Graduation from an UGC recognized college/university.55% is the cut off and please be careful when you declare this because if your aggregate is 54.9, then also it is rounded down to 54% only.
3.This competitive exams includes Language skills in English (you would do well with the B.A English background) both in the preliminary and the Main component of the exam. The other areas of focus include reasoning ability, aptitude for computers and numbers and general knowledge.
4.Joining a
MBA course and preparing side by side can be done provided age is on your side. If you need a government job and age is not on your side, it would be better to prepare seriously for the banking and other competitive exams, then get the job. Once you get the job, then you can always do your MBA by distance mode from IGNOU or an UGC recognized university.
5.There are many coaching centers and online resources available to help you prepare for the exams. Here apart from knowledge, practice in mock papers and timing yourself helps.
6.You can find study material from
http://bankexamportal.com/study-material
http://www.ibpsrecruitment.in/ibps-exam-study-material
http://www.bankersadda.com/
There are free apps related to general knowledge and current affairs, that you can download for use when you are travelling or on the move.