The Navy's officer program will accept you if you already have a biomedical engineering degree into one of their direct entry programs (like Officer Candidate School), but if you want to go to college on a Navy scholarship, then they only provide scholarships for those areas they have the most need. I would recommend getting a mechanical engineering degree, which is one of these areas. Many people minor in biomedical fields while getting a BS in Mechanical Engineering,and there is a lot of overlap in topics. Good Luck!
Mary (Missy) Cummings
Director, MIT Humans and Automation Laboratory