B.Com

It's not that B.Com is a good choice to go for Bank Job and BBA is not. Because, bank jobs do not have any relationship with the subjects under B.Com or BBA course.
But, you should be a graduate in order to be eligible to apply for Bank PO Jobs. PO - Probationary Officer is considered as Assistant Manager in the Banks.
Hence, you can opt for any of these courses at graduation level as per your interest.
One cannot get the position of Bank Manager directly. Only people who have worked on various roles in the Bank will be given this position. It would take minimum 10 years of time for the candidates to achieve this position.
Hence, get into the Bank job first. The entry level job after completion of graduation is PO.
IBPS stands for Institute of Banking Personnel Selection will conduct a Common Written Exam every year for the recruitment of PO positions across all public sector banks.
There is a huge competition for this Exam. Hence, one should have strong preparation towards all the areas of written exam to get through it and to score more marks.
After completion of written test, depending on the cut off, you will be called for Interview, which is the 2nd phase of selection process.
If you get through Interview as well, you will be given job opportunity as PO in the respective public sector bank.
The written exam consists of questions from the following categories:
-Reasoning
-Aptitude
-General Awareness
-Computers
-General English
You will not come across these subjects either in B.Com or BBA except English subject.
So, what I suggest you is join any of the course in Graduation as per your interest and start preparation for IBPS PO Exam from the very beginning of your Graduation.

Students who have successfully completed B.Com (Hons) can go for many higher level courses. As to join courses like MBA, MCA, LLB, etc., candidates will have to appear and qualify certain entrance exams like CAT, AIMCET, CLAT, etc. Some of the higher studies options after B.Com (Hons) are mentioned below.
CS
CA
CRISIL Certified Analyst Program (CCAP)
Diploma in Banking & Financial Services (HDBFS)
Executive MBA
Executive Program in Applied Finance, IIM-Calcutta
I.C.W.A. (2 years)
International Post Graduate Diploma in Risk Management
LLB
M.Com
Masters in Financial Management (MFM)
Masters in Management Studies (MMS)
Masters in Retail Management
Master of Business Administration (MBA)