Bioengineering is a field with good potential. However a Master's would likely add much to your chances of getting a job. I see the fields for a Master's program near you, and although not in biomedical, here is my suggestion:
Information technology would be my choice as many researchers (including myself) are developing clinical decision support systems and most of these are either knowledge based systems or pattern classification, and data mining, using all kinds of software tools that are available, many of them open-source..
I have always had a job in biomedical for just over 40 years and am still involved in research on medical imaging and on clinical decision support. The important matter is having a strong engineering degree and apply it to biomedical problems. Biomedical projects are frequently an applications of some engineering concepts, either electrical or mechanical.
When you finish the B Eng. try to enroll in a Master's that can be applied to solving a biomedical problem and perhaps you could have a co-supervisor from another university who is an expert in that area.. Today with the internet, much long distance work is possible.
Distinguished professor, Carleton University, Canada
PS If you go to google scholar and put my name, you will see several of the articles in the fields I mentioned to you.