BBA

Yes, you can do it. A candidate is eligible for enrollment to any of the level(s) of the Intermediate (IPC) course on passing the Common Proficiency Test and Senior Secondary Examination (10+2 examination) conducted by an examining body constituted by law in India or an examination recognized by the Central Government as equivalent thereto.
Students who are pursuing their final year graduation course can also register for the Intermediate (IPC) course on provisional basis and such students registration would be regularised and they can commence practical training only on submission of satisfactory proof of having passed graduation examination with the specified percentage of marks within six months from the date of appearance in the final year graduation examination.

What exactly is you job profile? If you want to apply for B.Ed, you can certainly do so, but as far as teaching is concerned, you will be only eligible to apply for teaching in class I-VIII.
A graduate with a B.Ed is not considered eligible to apply for teaching in Higher Secondary Schools or Colleges.
To be eligible to teach in colleges/universities, apart from holding a Master's degree, you will have to qualify National Eligibility Test for Lectureship or the State Eligibility Test for Lectureship, both conducted under the regulation of University Grant Commission.
I would suggest you go for MBA after BBA as MBA does not restricts you to any particular sector and you can avail a lot of opportunities after completing MBA course from a good institute.