BSc and MSc courses are offered in different subject by numerous colleges in India. BSc is usually a 3 or 4 year UG degree and MSc is a 2 year or 3 years PG course. As you haven't mentioned the subject which you want to study in, I am mentioning the names of the colleges in Bangalore:

Mount Carmel College, Bangalore

St Johns Medical College, Bangalore

St Joseph's College, Bangalore

Indian Institute of Psychology and Research, Bangalore

NMIMS Bangalore - Narsee Monjee Institute of Management Studies

For more colleges you may visit the link provided below:

https://university.careers360.com/colleges/list-of-msc-degree-colleges-in-bangalore?degree=B.Sc.

I hope this answer helps. All the very best for your future endeavors!