I have done my BBA from Jaipur National University. Am I eligible to pursue MBA now?

Yes, you are eligible. You can sit for any MBA entrance like CAT/MAT/XAT, etc.

Yes. Why not. For your knowledge, I would like to share that BBA is generally not considered as a degree. It is mandatory to be succeeded by MBA as if you think you can opt for any other Master's degree than MBA, you won't be called eligible for it as an undergraduate. So please go for MBA.