As a BME in his last year, I would say don't go there. BME itself is just a mixture of other engineerings~ and the pluses of a broad based education come with the negatives of the fact that you never delve deep into any one topic. You'll find soon that a company would rather hire a EE,MAE,CHEME for parts that need them. Kind of sucks, doesn't it? To watch all of your friends go to the companies that you are interested in yourself. Of course when desiging that circuit, an EE with 4 years of education in that is a far better option than a BME with 2-3 courses in circuits total. Its much easier to teach biology and have them read about it then to teach engineering. Hiring managers are also often unfamiliar with BME and go with what they know - which is the traditional Mechanical, Electrical and Chemical Engineers.
Of course before you think I'm bitching about BME and I am a failure bla bla bla. Let us say I have my ways and I'm pretty confident I'll be working next year Of course I also know that personally I want a higher degree (phd ftw!!!) for my personal satisfaction. But I don't think I'll go there until I work
Another problem like others mentioned is that the field right now requires MS and Phds for many jobs. Its very hard to get a job straight up at as a BS. I know friends that have found them - but "Entry level" really isn't much of an option. They want MS and PhD candidates. As BME as a whole (which is damned hard to characterize!!! The official definition adopted by whittaker translates to "anything related to thinking and the body") is still developing as is seen by the ever morphing curriculum at college campuses, and hasn't really moved into an "engineering technology"~ much of it is still "Engineering science". Areas like prosthetics (borrowing heavily from MAEs since a lot of elastic approximations of bones can be made) is very much in the technology ground, but other areas like tissue regeneration is almost exclusively academia and science right now.
If you really want to be a BME start off as an undeclared engineer. Then when you figure out what interests you in BME - take the most appropriate path of either ChemE,MAE, or EE. If you are interested in Biomechanics you will most likely go MAE or MSE as a pathway, if you get more interested in pharmaceutical application or tissue engineering (be prepared to go for a phd and spend your life in academia although it is incredibly interesting...), if you are more interested in signaling you will probably go EE. None of these paths are the only method - and there are many other facets of BME (computation, or even databasing for genetics) that doesn't necesarily involve actually chopping up the body. BME really is just anything dealing with "ideas and the body"! Once you have that, pack on a "BME minor" if your school offers it; if not, there are always electives in the biomedical related topics, and biology courses itself. That is really the best way to prepare for a path in BME. And that is the path - had I known it - that I would have taken