Is it possible to study an MBA as a Bachelor in Computer Science?
There is usually no specific subject requirement for a MBA. However, MBA programs usually require a few years of work experience (on average candidates have 5+ years). Often you will also need to get a good score on the GMAT test. But this is stuff you can study on your own, you don't necessarily need to take any courses.

I would think if you were interested in an MBA then you would probably be pursuing more management related opportunities anyway. But these could certainly be obtained by starting in a software engineering role and working your way up. Obviously you are not going to get a management position fresh out of university, everyone needs to start somewhere.

The company you work for may even pay for your management training if they believe you have promise.

You can read about the requirements and admissions process at various top MBA schools:

Cambridge Judge Business School

Harvard Business School