CX has two business class (and elite) check-in counters. Check-in shouldn't take more than a few minutes. However, if you have bags to check-in, you will need to stand in line to get them screened (xray) prior to check-in. This line is the same for all passengers regardless of class of service or elite status. If I remember correctly, you should now be able to use any available screening line which should definitely reduce the time it takes to screen your bags.

Once you check-in, you will need to clear immigration and customs which could take anywhere from 15-30 minutes on average.

Since BOM has seperate security checkpoints for each gate (there are a couple of exceptions where 2 or 3 gates share a security checkpoint) the line moves pretty fast and shouldn't take more than a few minutes.

Plan on arriving at the airport no later than 2:30am/2:40am and you should be fine.