I applied online through their website after seeing it in my school's job database. Then I got an email some days later and took an online IQ test. It was easy -- rotate the shapes, "count the number of t's in this paragraph", simple java. Phone interview the next week. Easy data structures and algorithms questions. Since I was unprepared I was surprised to be invited to an on-site interview two weeks later in New York.
Bloomberg was nice and paid for my airline and hotel, even though I got the details literally the day before I was supposed to fly out. I got a $100 gift card to reimburse my taxi and food. The office in midtown NY is beautiful. There are rows of computer desks (no cubicle walls), and lots of beautiful glass meant to embody transparency. The free food is in the plaza entryway, but just snacks and drinks. Delicious but can use more healthy stuff.
I had two interviews. The first was with two nerdy R&D guys. Two brainteasers and two programming questions, not difficult if you have been doing practice questions. The second interview was with one guy, a manager type. He asked me some questions about my resume and a simpler programming question. I liked him more.
Even though the office looks new, inside the culture still felt more like old Wall Street than Silicon Valley. Admittedly I was biased by the reviews on this site (about proprietary and outdated sw) which was only confirmed by my visit there. The career path was also not appealing nor was it explained very well to me.