Depends on what you mean by person in biomedicine and what job function you see yourself being in.
if you want to be a doctor or surgeon you'll need a medical degree. if you want to do biomedicine research in a lab you'll need at least a Bachelors degree in Biology or Biomedical engineering. Research positions also usually want advanced degree's such as Master of Science degrees or Ph. D.
Engineering needs a lot of advanced math so you have to be strong at, and genuinely enjoy, math to be a biomedical engineering. Scientists use less more and more specialized biology. In all cases you should get at least a Master's degree if you are interested in research. So at least 6 years of college. If you want to work in Industry then you can start at a Bachelors degree and see if you want to go further depending on your individual circumstances. Biomedicine/Biomedical science is a growing field with great positive impact on society so it's good to be interested in it.