Hey.

Yes, LLB degree is a wise choice after a BBA degree. Many people combine these two degrees. If your major goal is to crack UPSC exams you can even take it without the LLB degree as many people attempt UPSC after an undegraduate course. But if you still persist to pursue Law, you can go for that too. As various candidate pursuing law prepare for UPSC along with their degrees. You'd be able to attempt UPSC in the final year of Law degree till then you can prepare along with your degree.

Best of luck!