BMM Eligibility

Yes, you can as M.A. Is a specialised course in which aspirants are offered in depth knowledge of the discipline they have selected. Candidates can pursue an M.A. As a full time course or even as a part time course. M.A. Courses are also offered by many colleges in the correspondence or distance mode. A Masters in psychology, particularly with a specialised focus catering to a particular clinical need, opens the door to a variety of exceptionally lucrative professional opportunities. In addition to being personally and financially rewarding, these opportunities accumulate valuable experience for a wide range of other positions. Here are five of the best Masters degree programs to pursue after acquiring your Bachelors in psychology
1)Social Work
2)Counseling
3 (Criminal Justice
4)Health Sciences
5)Psychology.

As per UGC NET 2019 Eligibility you are not eligible on the basis of B. M. degree only. The detailed eligibility criteria is as under.
1. Age:- He/ she must not be more than 28 years as on January 1, 2019 for applying for Junior Research Fellowship. A relaxation of up to 5 years is provided for candidates belonging to reserved categories.
2. Academic Qualification :- For candidates who wish to appear for NET 2019 conducted by UGC, they must clear all the defined standards. Given below is the eligibility criteria to appear for NTA UGC NET 2019:
Candidate must have scored at least 55% aggregate marks (50% for SC/ST, OBC- NCL, PwD) in Masters Degree or equivalent examination from university recognised by UGC in Humanities (including languages) and Social Science, Computer Science and Applications, Electronic Science etc. To be eligible for UGC NET 2019. Candidates who are presently in the final year of their Masters programme or those who are waiting for their final year results can appear for UGC NET 2019 test.