regarding your particular major for job prospects in patent law, it depends on the type of patent law. if your interest is in patent litigation, the major is less important. if it's for patent prosecuation (filing patents), then the demand is tied more to the number of inventions filed in the particular field (electrical, mechanical, chemcial, etc). some fields like biotech (ie: pharmaceutical) really require a PhD. Also consider what type of biomedical/bioengineering you are.. this program in some schools has more bio/chemistry emphasis with some engineering on top (competing with the PhDs)... other programs are more engineering with a few bio/chem classes (competing against BS degree holders).
I'd encourage you to do more research on this... There are dedicated patent law sites hobnobbed by patent lawyers than can give you better info