Hey, there
I think probably I'm more qualified than others to answer your question, 'cuz I'm an international student doing MS in BME now in America.
First of all, I'm from China, where I got my B.S in Material Sciences and a conjoint B.S in biology. I got admitted to the BME MS program at UAB with fellowship in 2006.
There were two reasons why I applied to MS, rather than PhD.
1) Let's be honest, it's really hard for international students to get into BME PHD program. Seriously, I would have ended up with a bunch of rejections if I applied to PHD programs. Unlike most science and engineering PHD programs, BME does NOT enroll international students quite often. You'll find the majority of grad students in a BME lab are Americans while in labs of other majors, quite often international students dominate. The reason may be complicated but the fact is pretty evident. The odds is against us. Even though not many chinese students apply to BME programs each year, those who do apply typically would submit applications to more than 20 PHD programs. And, in the end, most of them got a pile of rejections only. Those few lucky guys can usually only get one PHD fellowship.
2) For MS program, it's much easier to get into, even though financial aid is typically unavailable, especially at the point when you got the admission. It is quite possible to get a research assistantship in the 2nd semester. If you're qualified, you can even get an assistantship outside BME department, say from mechanical or chemical engineering department.
I think it's better to jump into the pool, if you wanna learn how to swim, rather than practicing in your bed. So, I went ahead with MS applications and got a handful of admissions without financial aid and only one with fellowship ( I withdrew all revolving applications after getting the fellowship).
If financial aid is your top concern, many alternatives are available, such as PHD programs in Mechanical, Materials, Chemical, etc. They are much easier than BME to get in and they carry a full financial aid package for newly admitted PHD students. After getting admitted, you can always choose a research advisor doing BME research.
If you do want to get into BME MS program with full financial aid, based on my homework in 2006, only two programs are for you. The 1st one is John Hopkins' MS program and the 2nd is the one at UAB.
At this point, I'd suggest you contact individual faculty for RA positions. Many BME PHD programs offer fellowships for 1st year students and they have to secure a RA position in the first few semesters. In such a case, technically, you have to have a faculty endorsing your application, who is your "potential" advisor after you get admitted, during the admission process. Otherwise, it's quite possible to get rejected.
To be honest, funding is becoming more and more hard. International students are not eligible to receive funding through federal government. As you know, many research projects are supported by National Institute of Health (NIH) and so we can't take RA if this position is paid from a NIH grant. So, basically, only University/grad school fellowships or faculty's funding from private source can be used to hire us.
Another thing is the economy. About 5 years ago, NIH got a huge amount of money from the appropriation to support biomedical research. Now, the money is up. What's worse, the Whitetake foundation was closed a couple of years ago. The new tenure-track faculties in my department are suffering from these things. If they can't get a grant, we can't get a RA.