Allardyce spent nine years with the club as a player in the 1970s and won promotion to the Premier League during an eight-year spell as manager from 1999.
The 62-year-old led Bolton into Europe for the first time in 2005 and the club finished in the Premier league's top half in four successive seasons under Allardyce.
A bag of treats from Bolton bakery Carrs Pasties were delivered on a tray to the former manager.
“I had a great time there. My great dreams became a reality for me at Bolton," Allardyce said.