Keep in mind that you are admitted based on overall GPA and MCAT as the main factors for med school. Major does not matter as they are people applying from many different backgrounds. Do BME if you have an interest in the major, otherwise, don't suffer through an engineering curriculum, its very unforgiving for those who aren't fully interested in it.
At my school, a HUGE amount of people are in Bio. Most want to be doctors. I do know people that are in Psych that are gonna take classes to fill the med school requirements for application!