It can be seen on a rack in the Clothes Shop once moused over.
Bambadee made the Friendship Bracelets, and always wears his own.
There was a glitch when you walked out of the Book Room by doing several actions, there would be a giant friendship bracelet hovering in the air. However, it was removed after the July 2008 server updates. This also worked for the Captain's Quarters Key.
This item is placed in a similar manner to the Captain's Quarters Key (both are situated at the end of the book) as both books were written by Rockhopper.