A Masters degree is a big step and requires careful planning and thought. I would advise having a look at courses that are available locally and then making a decision based on what you are interested in and think you personally would get the most benefit from (both from a personal and a job market point of view). For a commitment like this a personal interest is very important.
Also bare in mind that (in most countries) if you have a Masters degree your employer has to legally pay you more than someone with just a Bachelors degree. This can actually LIMIT your future job opportunities as an employer may choose someone less qualified over you to do a job if they do not see the benefit of a Masters degree qualification to their company. This is one of the main reasons I never went for a Masters degree.
Perhaps a certificate would be a better start if you are unsure, many can then be cross-credited to a degree or masters if you wish to pursue a more advanced qualification.
I suggest you get some graduate catalogs from different universities that offer MS and PhD programs in Engineering. Take a look at the fields offered and what the entrance requirements are. Decide what fields are interesting to you, and which schools you think you'd like to attend. Do a web search for fields that are currently in demand; if it takes you a couple years to get your Masters degree those fields will likely still be in demand once you have your degree.
A BSME is an entry point for various specializations. Are you analytical; does finite element analysis interest you, for doing stress analysis? Thermal analysis? Or is CAD and packaging more your thing? How about Aerospace? Or Robotics? Maybe you are interested in leading an engineering team, so perhaps Systems or Project Engineering?
You might even consider switching fields entirely, to electrical engineering or to a 'pure' science like Geology or Optics or Astronomy.
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