|Don't ask to ask, just ask|
I went the academic route into Bioinformatics - BSc in Biochemistry, then a PhD in Molecular Neurobiology. The fields of Bioinformatics that I'm familiar with are DNA/protein sequence analysis, expression analysis, genome and genetic analysis, protein protein interactions/pathway analysis and 3D structure analysis. I have been using bioinformatics since 1988 so I was lucky enough to be in before bioinformatics was thought of as a buzz word.
After 7 years of postdocing I found a job with a reasonably well known bioinforamtics company that produces both desktop and enterprise level bioinformatics software. To do all that I had to pick up a lot of Maths, a reasonable amount of Perl and skills in *nix, relational databases and diverse other computer/techie things
Finding folk with these skills sets is not easy. Most of my hires have a Batchelors and a Masters, PhD or Masters and PhD combination. The main reason for the heavy educational background is that to be a competent bioinformaticist, you need to have the experience in doing the biology as well as the computers - this takes time. I also tend to look for actual real projects, eg show me your source code/database schemas, where are your papers, etc. For me this is the main way to screen out folk who can do it, not just talk about it. You might look into certification programs - the best one that I know of is in Montreal - the Canadian Bioinforamtics certification program http://www.bioinformatics.ca/. It has an excellent combo of hands on training and theoretical background that you will need to pursue bioinformatics usefully. Otherwise pick a course that allows you to carry out projects that have real goals/results and hopefully publish papers. This is really the best way of getting your foot in the door for this field.
I am thinking of taking a Masters in Maths at this point - I find this a lot more interesting and difficult than doing a Masters in Computers/IT, but that is my personal bias. Part of that bias is that I'm not too impressed with the product of many 2 year Masters level IT programs in Colorado - they are rather too cooky cutterish and produce folk with some knowledge, a lot of not very grounded opinions and little practical application in tackling real problems. A Maths degree is (hopefully) less popular so I hope it will be a bit more applicable to my current needs.
If you want a starting reading list, try the following:
Two other titles that might be entertaining:
In reply to Re: Advancing oneself personally and professionally as a programmer (discussion)