Applied online to the Financial Sales and Analytics Training Program on the Bloomberg site, an HR assistant emailed me the next day to schedule a phone interview. I made the phone interview for early on the following week. After the phone interview they called me back 3 hours later offering to fly me into NYC for a 2nd round interview at the Lexington Headquarters. I flew out to NYC the following week; they paid for my flights, paid for 1 night in a nice hotel, paid for accommodations to and from the airport in a Lincoln Town Car, and finally gave me a 75 dollar gift card to cover any additional expenses (I know right! Sweet!).
I showed up that morning and was taken in for a 2:1 interview. They asked me common questions but focused on the fact that I was interested in the global economy/markets and there would be great room for advancement for me at their company. Afterwards I was taken around, given a tour of the building, the Bloomberg tools were explained to me, and finally I shadowed several employees performing day-to-day functions.
There were about 6 other prospective employees there, we were then dismissed 2 at a time and all of us were presumably told we would get a call back in 1-2 weeks. It's day two of the wait for me so I'm not worried yet.