Can I get into a Good Master's Program in Bioengineering?

You should be considering PhD programs, not MS programs. Many PhD candidates get paid to go to school through grants, teaching or research assistant positions. Many PhD programs will grant a MS as a consolation prize if you don't complete your dissertation, and some programs don't allow applicants for the Masters degree directly unless they are first admitted as PhD candidates. In any case, if you qualify for the PhD program, you'll save a ton of money and have a lot more options for research. You don't need a masters degree to apply to many PhD programs.