This is a very good question! Certainly people with degrees in computer science, electrical and mechanical engineering, and even construction management work in environmental and (with the exception of construction management) biomedical engineering. If you are definitely going to attend a certain college, my suggestion would be to look at the web sites for the individual departments or make an appointment to talk to a faculty member or undergraduate advisor in each department and find out what kind of courses are offered and what kind of research the faculty members are doing. Both environmental and biomedical engineering are very broad fields, as you probably know from your research.Environmental engineering can range from designing and building treatment systems for solid, liquid, and gaseous waste to collecting and analyzing samples and running computer models of how pollutants travel through the air, water and soil. Biomedical engineering includes the development of medical devices that involve electrical and mechanical components such as artificial joints, stents and pacemakers, and drug delivery devices as well as protective equipment for soldiers, workers, and athletes.
Today in many mechanical engineering departments you can find faculty members interested in biomechanics, applying principles of mechanical engineering to bones and joints. Some mechanical engineering departments also offer courses in green engineering that include topics such as life cycle analysis and energy management. So, mechanical engineering may be your best bet, but it would be worth talking to some people in the other departments as well just in case there is a faculty member in another department with interests similar to yours. Good luck!
ENGINEERING - MECHANICAL: BS
ENGINEERING - ELECTRICAL AND ELECTRONIC: BS
Mechanical Engineering is probably a better match if you are interested in Biomedical Engineering. Many ME programs have courses in biomechanics. In addition, if you choose to go to graduate school in BME, then most programs accept UG degrees in Mechanical Engineering. The next option would be Electrical Engineering (many EE's are used to design instrumentation for hospitals, etc.). EE is also accepted as an UG option if you choose to go to a BME program for graduate work.
Hope this helps some!