Hello,
Admission to BMS course is offered based on 12th std percentage college releases its merit list first. St. Xavier college, Mumbai has separate criteria they conduct an entrance exam for this course. You can go to the website of the University of Mumbai and check the link for admission to various colleges.
Here's a list of college which offers BMS courses in Mumbai
1.Wilson College, Mumbai
2.HR college of commerce and economics, Mumbai
3.Jai Hind College, Mumbai
4.KJ Somaiya College of Science and Commerce, Mumbai
5.Bhavan's college, Mumbai
6.Mithibai College Mumbai
7.Thakur college of science and commerce Mumbai
8.Lala Lajpat rai college of commerce and economics Mumbai
9.KC college of arts, commerce, and science Mumbai
10.Vidyalankar school of information technology, Mumbai.
Here I am providing a link you can check out the details of the colleges.
https://www.bschool.careers360.com/colleges/list-of-bms-colleges-in-mumbai

Hope this will help, All the best.!!