The process started with a "take home" coding problem (given an article, write a program that computes how many times each distinct word appears). Fairly easy problem, and you can use any language of your choice. No time limit, but it should be doable in a couple of hours.
It was followed by a phone interview with a manager. The conversation was actually completely non-technical, and mostly involved finding out "why" I made the choices in my career and how I dealt with certain professional situations. He also asked about my opinions on where my current company is headed in its industry, and its high level business strategy. What they wanted to see is if the candidate has strong opinions on a subject, and whether he/she can articulate and communicate these ideas clearly. Bridgewater's culture is heavily based on "truthful" communications to the point of brutal honesty, and the interviewer's attitude reflected that culture quite clearly.