I can't speak for all schools, but at UC Berkeley, the majority of bioengineering is not, in fact, bioengineering. You will probably spend much of your second year and some of your third year taking classes that either are in, or are cross-listed with mechanical engineering, materials science, civil engineering, nuclear engineering, electrical engineering, and computer science.
It's only really in the latter part of your third year and fourth year that the majority of your classes will be true bioengineering classes (that aren't cross-listed with another engineering department). It's basically because bioengineering classes have pre-requisites that span across biology and nearly all of the engineering departments.
As a major for pre-med students, if you can handle the workload (and if you take the standard route, it is a VERY heavy workload) you'll end up with a very strong foundation for biomedical research and medicine in general.
On the other hand, make sure that you're ready for a biology/engineering combo major. The most difficult part of bioengineering isn't the individual classes. Each class, in and of itself, is relatively straight forward and easy for the members of the associated majors, but for one person to master the mindset and methodology required to excel in all the engineering departments as well as the biological sciences, you have to be able to adapt to different styles of instruction and studying.
Not only that, but if your classes are curved, you will be taking classes in nuclear engineering, or computer science, with students who are nuclear physics and computer science majors, and to get the same grade as them, you will have to do just as well despite not having as much pre-requisite training.
In the end, I would highly advise you to go into bioengineering only if you absolutely love math, physics, and biology all together. Otherwise, the sheer amount of time it will require of you to stay on top of things will detract from your ability to pursue extra-curricular activities and research.
If you're curious about the bioengineering industry itself, bioengineers can be found in almost every sector of engineering. The only jobs that are specific to bioengineers though are usually those from biotech companies. Sometimes it can be engineering drugs, or designing the factories that will make pharmaceutical products. There are relatively few jobs available currently that involve nanotechnology and advanced robotics, as right now most of the work being done in those areas are research labs (perfect if you want to go to grad school) although those fields could open up rather quickly to the mainstream public in the coming years.