I am a passout from BMSCE and I came through COMEDK so I can answer this question. I dont know the latest fees as they increase after every 2–3 years. I am from 2012-2016 batch. So at my time the hostel and mess fee together was around 1lac 10 thousand. This is the fees for hostel outside campus. Inside campus hostel fees is little higher.
The college fees was 1lac 60 thousand per year.
Tip: The hostels get full very fast. So book a room just after counselling. I didn’t get hostel so I had to live in flat nearby. But beleive me hostel life is way better in BMS because they have lots of activities and interactions which you won’t get staying outside