There are many different options for a BME degree, and you do NOT need a PhD to get a "good" job. Here are some career options for BME majors:
Biochemical: this might involve pharmaceuticals, manufacturing drug delivery systems, vaccine development, or ensuring quality control.
Biomaterials: you'd help design and develop medical devices, manufacture them, and ensure quality control. Examples include creating or improving artificial skin devices, heart valves, or joint replacements.
Biomechanics: this might involve design, develop, and test medical devices, such as prosthetic limbs, surgical tools, cardiovascular implants, or optics.
Bioinformatics: this involves computer programming/statistics where you'd be organizing and analyzing lots of data. You might write a program that searches for certain patterns in someone's DNA for example.
There are also many other options that many BMEs go into, such as consulting or another engineering field such as mechanical engineering, chemical engineering, or electrical engineering since there can be so much overlap with these fields.
I work with engineering students, and the stereotype you may hear is that BME is too specific a field or, alternatively, too general a field, so people have to go to graduate school. This is not true. What IS true is that BME is not a clearly defined, structured path (although hardly anything is these days). It is very versatile and you can go into almost anything you want as long as you seek out the experience for it (by this, I mean take electives in what you want to specialize in, find internships in fields you want a job in, join organizations where you work on projects related to your interest area, network at your school's career fairs and information sessions, etc.).
Feel free to go to your school's career advisor to find out more, and don't be afraid to take advantage of BME's versatility!