Many students also use a Bachelors in Health Science as a springboard and pursue entry into Medical School, Pharmacy School, Dental School, Nursing, Physical Therapy, Speech Therapy, and Occupational Therapy.
With any degree, it's best to start planning for entry into the job market while still in college. Visit your college's career center and discuss your goals. If, for example, you want to pursue research positions upon graduation, you perhaps could start interning at the hospital affiliated with your school or for one of your professor's research projects. For any job, you want to have some relevant work experience (either part time, during summer breaks, volunteer experience, or an internship) so you can start building the skills that those positions require.
Another good resource is your Academic Advisor. Many schools have advising departments by major, so you can look up who your advisor is and make an appointment online. If you are pursing further schooling after you undergraduate degree, they can make sure your major and elective courses meet prerequisite requirements for entry into your chosen graduate school program.
Meighan has some great suggestions, and I'll add on to her response, specifically to consider the information that you added in your comment. A couple of short-term options would be to look at temporary staffing agencies to find a role as a contractor, if you're having a hard time getting hired into a permanent position. Another idea is to look for 'internships' that will accept students after graduation.
Your college's career development office may be another resource for you on this.
Personally, I wouldn't recommend going back for a masters without getting some real-life work experience, unless you make a concrete plan for how you will get work experience as part of your masters program. Otherwise, you will have even more education and potentially still no work experience to use towards employment (and maybe even more student loan debt). Plus, after working for a little while, you may find that you are passionate about something different and decide to pursue your masters in a different field.
Are you on LinkedIn? I'd recommend signing up and using your network to help introduce you to people within your field or at companies where you'd like to work. Having a personal connection goes a long way in helping to find a job. Don't get discouraged - the job market is tough right now, and you're doing the right thing!
All the best,
And if you complete this program you might be a
Occupational therapy assistant
Physical therapy assistant
Registered health information technician
Biomedical equipment technician
Medical lab technician
All the Best!