Can you do all the accounting related tasks with the BBA alone?
Yes, if you went to a decent school and earned good grades.
What extra accounting related things can you learn in MBA course?
For example - more in-depth studies in various aspects of taxation, also data visualization, data analytics. Best if you review the MBA accounting related course offerings at the college you are interested in.
I have an MBA and I'm currently a CPA candidate. You do not need an MBA to become an accountant, I just went for mine because I wanted to have more diversity in my education and I LOVE business as well as accounting. If you sign up for a good study review course that will help cover everything you need after college. I'm currently using UWorld Roger CPA review and have loved it.
I think if you're looking to work in the accounting field you should aim towards a CPA rather than an MBA. A CPA is so much more helpful in finding a job in general than an MBA. If you already have a bachelors in accounting try and sit for the CPA exam, get a good review course, study well and that's it.
In terms of a good CPA review course, as someone else mentioned in this post, Roger CPA review is a phenomenal course. Highly recommended!!
Post grad and certifications of course don't work against you. But neither will be helpful without being able to network yourself into an interview or in some cases around the interview process entirely. Joining professional groups / associations and building an online presence are indispensable to developing a career path. We get caught up in the idea of leaning on credentials, but they can only get a person so far in the job search.
I see that the OP is in India. So, of course take into account the unique sociopolitical climate that exists there. I have professional colleagues whose background is Indian, and I know they would agree that the old "systems" haven't disappeared. I won't get much further into that since that's a sensitive subject.
In any case you would agree that the adage of "who you know" is true anywhere.
Another factor is that since it sounds like you're looking for your first accounting job, I would make sure it's a job that requires at least an undergraduate degree. Otherwise the experience won't be much in terms of resume building.