After applying through Bloomberg's website, I received an email about a week or two later saying that I had made it through a round of resume screening and I was asked to take an online skills assessment test. This test consisted of basic IQ sort of things (shape rotations/reflections), or things you might see on the LSAT exam (given 8 statements, what order did the horses place in a race?)
2-3 days after the IQ Test, I was asked to set up a phone interview which took place the following week. Because I don't have a computer science background, they asked "Get to know you" type questions about my past experience, and then asked targeted questions that are basically round-about ways to get you to consider computer science problems.
Within a week I had been asked for an on-site interview, which I went to a few weeks later. This interview consisted of three stages. In the first, I met with three interviewers who asked me questions to gauge my understanding of algorithms and high level design, and they asked me to write down a program in full syntax for the language I had the most experience in (Java). In the second round, I met with a senior member and he asked questions to gauge my interest and fit with the company, as well as to gauge my ability to transition into an IT position from an engineering background (What makes you think you would be happy doing this type of job every day when your experience is primarily in research?) The third and last round consisted of meeting with a man from HR and he asked very general questions, then gave me a super-brief tour around 2 floors of the building.