Realize that biomedical engineering covers an enormous range of knowledge areas. A degree in biomedical engineering will require biology, math, multiple sciences and knowledge of mechanics as well. You won't have to limit yourself to being only a biomedical engineer, but can probably do just about any engineering job. My original degree was in computer science, after which I went into electrical engineering. But I eventually found work in medical devices, and just about every aspect of my education came in handy at one point or another. Staying flexible and willing to solve any problem will create a lot of opportunities for you. My advice is to stay curious.
Great question! I was wondering the same thing when I was applying for jobs. There are so many different directions that you can go with a biomedical engineering degree. I personally volunteered in a hospital, worked as a medical device engineer, and I am now working as a consultant. While some of my classmates went into traditional engineering positions that involved medical devices, organ transplants, cell research and other jobs along these lines, others went into more business focused positions such as consulting, investment banking, and private equity. You might also consider research or continued education.
Amelia recommends the following next steps: