Colleges in West Bengal

Both are much respected institutes. Joining either of them would not be regretted.
You should consider other factors such as the location of your home town, branch you are getting, placement statistics, importance of NIT tag to you and then decide.
I can tell you 1 thing for sure, i.e. joining NIT-B

Yes, you can definitely go ahead and fill the form for your course now. IIBS does not only accept MAT, but has its own set of entrance exam laid out which is not too difficult at this level. You should definitely keep this is as an open option.

Must have mathematics, physics and chemistry in 12th class and marks should be above 60%.
(Entrance exam or direct admission)

You can't get any NIT with this rank. Please try and work hard again. Best of luck.