B.Sc

Yes, you can pursue M.Sc. Veterinary microbiology after B.Sc. Microbiology. There is an entrance exam in colleges to get admission in the post-graduation courses. The eligibility to apply and appear for those entrances is clearing your graduation with a minimum of 50% aggregate in B.Sc. The colleges that offer M.Sc. Veterinary microbiology in India are
Birsa Agricultural University, Ranchi
Veterinary College, Karnataka
Swami Keshwanand Rajasthan Agricultural University, Rajasthan
Assam Agricultural University, Assam
Orissa University of Agriculture & Technology, Orissa
G. B. Pant University of Agriculture & Technology, Uttarakhand
Faculty Of Veterinary Sciences, Kolkata
College of Veterinary Sciences, Karnataka
Rashtrasant Tukdoji Maharaj Nagpur University, Maharashtra
Kerala Agricultural University, Kerala
Jawaharlal Nehru University, New Delhi.

As fancy as a course of biotechnology sounds, what most colleges/universities offer in the name of biotechnology is life sciences. Yes, you heard that right. Biotechnology= Life sciences with a special focus on applied techniques like PCR, Western blot etc. (I. e. if you join a really reputed college). And that is not a bad thing. For e. g. in St. Xaviers Kolkata, you would study genetics, cell Biology bioinformatics, enzymology, immunology, ecology and evolution etc. In the Biotech integrated course. It gives you a broad perspective on a lot of subjects. Now that I have laid the groundwork, lets answer your first question:
You should continue with biotechnology because it gives you knowledge about a wide range of field. In case you want to pursue Ph.D. afterwards, it will help you to figure out what you actually like. It also acquaints you with a wide variety of applied lab techniques like PCR, mass spectroscopy, Western Blot, Northern Blot etc. This will help you if you want to join a company like Biocon. Besides, specific courses like Genetics, Molecular Biology biomedicine or any other course has the same practical course, so why limit yourself to one subject when you can broaden your knowledge. As for your second question, M.Sc. And MS are the same degrees with different names, at least in India. M.Sc. Is the name of the degree in India. A lot of Indian institutes like IISERs also use the name of the degree as MS. The degree might vary in other countries. In USA, MS means you are a Masters in engineering sciences. But in UK, its meaning is same as that in India. So in Indian context, there is no difference between the two. So there is no better option.