After BBA you can apply for IBPS exam. You can check the eligibility criteria given below.

The eligibility criteria:
You should have minimum 50 % in your Graduation to apply for the exam.

Your age should be 21 to 30 years.

Yes, you can apply for IBPS exam after BBA.

Below is the eligibility criteria of the exam you can check-

-Candidates must be a indian
-Candidates must be complete a degree in any stream from recognized university
-Candidates age limit between 21 to 30 years . Age relaxation as per govt rules.

Good luck!!

Assuming you are asking for IBPS PO then yes, you are eligibel to write this exam as candidates are required to have a Graduation (Degree) in any discipline from a University recognized by the Government of India/Any equivalent qualification recognized as such by the Central Government. Candidates must possess a valid Marksheet/Degree Certificate while registering online.

Hope this helps!!!