Like others said, check with your premedical or BME advisor. They should be able to show you the four year course schedule for your degree. Each med school has their own prereqs, so check on the websites of various schools then work with your advisor to map out your course schedule. Generally, the first two years of BME courses should cover most of the basic med school prereqs (they did at my school). You might have to take a few higher level med school prereqs (genetics, O.Chem II, etc.) and non-science courses as electives.
This is definitely something to consider. You might have to spend more time studying than you would if you pursued another degree, that time could be put towards ECs, studying for the MCAT, etc. BME is a good fallback degree and has some impressive research opportunities though. I will also say that my engineering coursework helped me out quite a bit on the MCAT with CARS and C/P