Hi, 

Yes a person with BCA or MCA can apply for bank clerk job. For bank clerk or PO any person with any degree can apply. Though for that you have to take up banking exams like IBPS which is a common entrance exam to get into banks either for clerk or PO. To clear that you can go to coaching centres and take up coaching or prepare at your own convinence phase. But a person with any degree can take up banking exams.

Good luck 

Hope it helps.