Do I have to get a B.Des degree if I want to pursue M.Des at NID?

No, it is not always necessary. An M.Des degree requires a 3 or 4 year undergraduate degree/diploma with a 55% aggregate. Following that, you must pass the CEED test or a university-specific exam. Some colleges additionally need a portfolio presentation and a personal interview. 

Colleges offering M.DES degree

1. Ambedkar University Delhi - Dr BR Ambedkar University, Delhi
2. DTU Delhi - Delhi Technological University, Delhi
3. HITS Chennai - Hindustan Institute of Technology and Social Sciences
4. IDC IIT Bombay - Industrial Design Centre, Indian Institute of Technology, Mumbai
5. IIITDM Jabalpur
6. IIT Guwahati - Indian Institute of Technology Guwahati
7. IIT Hyderabad - Indian Institute of Technology Hyderabad
8. IIT Kanpur - Indian Institute of Technology Kanpur
9. JMI New Delhi - Jamia Millia Islamia, New Delhi
10. KSD Ahmedabad - Khyati School of Design, Ahmedabad