Hi Siddharth,

St Xavier's Mumbai is not offering BBA this time but it offers BMS (Bachelor of Management Studies) which is more or less the same as BBA as both are Management corses.

You may check all the courses offered by St. Xavier's, Mumbai over here : https://www.careers360.com/colleges/st-xaviers-college-mumbai?utm_source=google&utm_medium=kg

Other Colleges offering BBA in Mumbai are : 

• Amity Global Business School,  Mumbai 
• HR College of Commerce and Economics, Mumbai
• KJ Somalia College of Commerce and Arts
• National Institute of Management 
• Tolani College of Commerce

Hope it helps :)