The Bridgewater interview is a very unique process. If you know anything about the company, they have pretty much redefined the term "corporate culture" and even border on cult. Everyone on staff, from the newly hired grad to the CFOs, are expected to question and scrutinize every decision made and continually strive for improvement.
That said, I got the interview after attending several recruiting sessions and private events (I attend an Ivy, so they recruit on campus). The interview is with 5-10 interviewees and 1-2 Bridgewater employees. A question is posed, in my case "Is television bad for society?", and the group is expected to debate. That's it. That's the first round interview. The BW interviews actively participate and the interviewees are expected to relentlessly pursue the "truth". Our group ultimately decided it was a positive source for society on a whole, while unfortunate side effects are created.
Still waiting on the results. Once they're in I can comment more on what they looking for in terms of your participation.