It's either 48 hours or seven days.
CBA FAQ: 67. What is the Amnesty provision?
The above makes it sound like it follows the rules of the waiver wire, which would mean the bidding process would be a full seven days (the number of days a player stays on waivers if released between July 1 and August 14). With that said, this past offseason, it was just 48 hours. I'm not sure whether that's the norm, or if it was sped up due to the condensed offseason.