There are plenty of collages in Mumbai, Maharashtra for BBA. 

1. National Institute of Management (criteria- 12th grade card and entrance test marks conducted by them)  

2. Amity global business school (criteria- 12th pass certificate and you have to qualify entrance test conducted by them)

3. Narsee monjee institute of management studies (criteria-12th grade and entrance test)

4. Universal Buisness school(criteria- 12th grade card and entrance test)

5. Institute of Business studies and research(criteria-12th grade card and entrance exam)

You can check details also  at- 

https://www.collegesearch.in/bba/colleges-mumbai

https://collegedunia.com/bba/mumbai-colleges