Hi There,
I actually started with my licencing process. I am going to be working in Melbourne though, so I can only speak toward the process to getting a licence in Victoria. From everything I've heard and read, if you had your education in the U.S. you probably won't have to do the bridging course. But I'm honestly not 100% sure. I would contact the NSW board directly.
But my timeline went a little like this:
July 2007: Passed my NCLEX/started working as an RN in a hospital setting
Sept-Oct 2007: Started getting all my paperwork together for the licencing process
Early November 2007: Submitted my application for licensure to the Nurses Board of Victoria
mid-January 2008: Received notice from the board that I had been approved
Jan-March 2008: Contacted hospitals and applied for positions in Melbourne, went for an interview in-person in Melbourne and was offered a position
Late March 2008: Started the Visa process for a 457 employee sponsored temporary visa
Hope that helps

I'm not sure the specifics about the different boards so I would contact them directly regarding bridging courses. But no, I did not have to take one.
Sorry, one adendum to this I wanted to add: Australian nursing boards only recognize BSN degrees, not associates. Its the minimum requirement for nurses to work in Australia. So if you have an associates, it might be a whole other story.