It can be seen on a rack in the Clothes Shop once moused over.
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.
Bambadee wears the Friendship Bracelet. He was the first one to wear it.
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.