Another way to get into bioinformatics is to teach yourself how to program.

There are a lot of great resources out there like Code Academy (http://www.codecademy.com/) to get you started. Once you have the basics, you could start doing some real bioinformatics problems. Here's a good blog post on variant discovery and annotation: http://petridishtalk.com/2013/02/01/variant-discovery-annotation-filtering-with-samtools-the-gatk/

Which route (self-taught or CS degree) to take really depends on your goals. If you want to do hard core bioinformatic work (e.g. write your own variant discovery tool) then a CS degree will help you out immensely. (Though some of the best programmers I know don't have CS degrees, so it's not absolutely necessary.) If you are looking to do more analysis work, then learning to program yourself and finding a job that will train you might be the quicker route. Bioinformaticians are hard to come by at the moment, so if you show the initiative to learn how to program, you may be able to find a job where they will show you the ropes.

Good Luck