One week after I applied they scheduled a phone interview. The phone interview was pretty standard, they asked me what I knew about Bloomberg, why I was interested in financial markets, etc. As long as you do some research on Bloomberg and read the news regularly, the phone interview shouldn't be an issue. Later I was asked to attend an in house interview in New York.
Bloomberg paid for my flight and hotel, and at the end gave me a $75.00 gift card to cover any additional expenses. The interview was with two managers, both seemed nice, though one wouldn't make eye contact with me, which I found a bit odd. They asked me questions similar to the phone interview, gave me some hypothetical situations, asked me how I would handle them. The interview seemed to go well, though I was a bit nervous.
Several days later I received a "copy/paste" email from HR with bad grammar, telling me they had decided to pursue other candidates. I emailed an employee who showed me around that day, asking if they knew why (I wanted some feedback, wasn't trying to change their mind or anything), within minutes HR replied to the email, saying due to company policy, they were not allowed to give me any feedback, and that I should direct all questions to them.
I wouldn't have been as irritated if they had bothered to make the initial rejection letter look like a human wrote it, I guess after getting such a good impression of the company, I didn't expect them to do something that seemed a bit unprofessional. Since they did pay for my trip to New York, I didn't get too upset about the lack of feedback. Aside from the issues with HR, everyone was very nice and it was overall an interesting experience, I would still recommend applying to Bloomberg.