Can I do my honors during MBA rather than BBA?

BBA is a UG (under graduate) and MBA is a PG (postgraduate). In order to pursue MBA, you need to have a degree from any institute and then have to write entrance depending on which college you want to join and then later you can take admission in MBA in any Institute.

Yes, You can do the same. BBA (hons. ). + MBA integrated course is a good option.