You will surely get BCA at BIT Mesra (off-campus) with an 89% in boards. However, I would like you to reconsider your choice of pursuing a BCA.
I am an alumnus of BIT Mesra (off-campus) myself. I decided to go for a BCA because I did not want to take a year drop to prepare for JEE, unlike the rest of my classmates. I do not regret my decision, I have a decent job that covers my expenses.
However, I do feel that I am doing the same thing after a six-year BCA with MCA that I could’ve done with a 4-year B.Tech (CS/IT). Also, I might have ended up earning more with an engineering degree. According to me, if you pursue your B.Tech (CS/IT) from a renowned institution like BIT Mesra, it will be more beneficial for your career in Computer Science.
Therefore, if you are from a Science background, I would suggest you to talk to a career counselor and find out if a B.Tech CS/IT will be more beneficial or not.