I think that a bioethics degree is something that is worthwhile pursuing because it is definitely something that we will need in the future. Bioethical issues are going to be something that we deal with as it comes to the integration of technology and other biological influences. Go for it.
There are easier degrees to pursue and other degrees that will open up a larger job market for you then a bio ethics degree. However if you are passionate and knowledgeable about the issue then you should definitely pursue the degree. You just need to make sure you are fully committed to it first.
As scientists make ever more advances in biology, it becomes more and more important to examine the ethical implications of our discoveries. A degree in bioethics will become more valuable in the future. Hospitals and research facilities will need experts in the field to help them make difficult decisions about biology.
You can do anything you want to do in life. If you have a passion for bioethics it is worth pursuing. It is definitely a controversial topic. The job market may be a bit rough compared to other majors but if you truly have a passion it is worth your time.
As with many degrees that can be pursued, one would be better to ask, what are the job opportunities in this field, with this particular degree. While there are positions available in this field, they are very few. Secondly, ethics (and bioethics) aren't always followed well by society and especially not by business. So, asking about the job availability and the actual job would probably lead someone to believe that there isn't must you can ethically do with a bioethics degree.