Biomedical enginieering is a great field because it is interesting, the work has a direct impact on the health of people and it is realtively high paying. I own a medical imaging company and know that Ph.D. s in BME are tough to find. Most students graduating with a strong physics background are prepared to start in the field without any focused training in the medical fields. In fact, Siemens prefers a strong general physics background only, without prior medical so that you can learn the "Siemens way". I usually seek Ph.D. with a good background in general physics and a dissertation in a particular branch of medical imaging. The BS is not very helpful, but the Masters is enough to get in the door. Ph.D. is ideal.
Here is what I recommend for course work:
1) Thermo/statistical mechanics. Most of medical imaging is optimization problems, maximum likelyhood, bayesian analysis, etc. Good background in statistical methods is helpful.
2) E&M. MRI is one of the fastest growing areas with most centers moving to 3 Tesla magnets. The quantum mechanics of spin 1/2 systems is also important.
3) CT. Being comfortable with non-cartesian coordinate systems is helpful in cone-beam reconstruction problems. Also the physics of photon absorption-re-emission is helpful.
4) Statistics for data analysis. T-tests, standard deviations, chi-square, population analysis, etc.
Radiation safety is hugely important. If you can do an intership at a facility the routinely handles radiation to become familiar with how to protect yourself and the public from radiation, that is great. Any hospital that provides radiation therapy will have a staff physicist for therapy planning. Also many cities in the US have commercial cyclotrons. Look up "PETNET" on the internet for some of their facilities.
Good luck!