Which course should I pursue after completing BBI course? Can I pursue MBA?

Yes, you can do it. But, MBA from good business school will be an added advantage. Prefer admission through CAT based or MAT based and you can join in a good B-school. So, you can get a good placement.

Yes, you can go for MBA after BBI. MBA in finance will be a good option after BBI. You can also look for other courses, as per your field of interest. You can think on Financial Engineering, Data Sciences, Operations.