The title for this episode is a pun on the title of the '70s television show The Bionic Woman.
The circumnavigation of the globe by the Planet Express Ship passes by some notable landmarks: the Golden Gate Bridge, the St. Louis Gateway Arch, and the Leaning Tower of Pisa. After the ship smashes a gap in the Great Wall of China, an invading Mongol horde immediately passes through it.
Gangs of savage children and adolescents are found throughout science fiction, including "Mad Max: Beyond Thunderdome", the "Escape from New York" and "Escape from L.A." films, "Logan's Run", and the Star Trek episode "Miri". Predating all of these, and notable as the decline into savagery is the entire subject of the book, is "Lord of the Flies" by William Golding. It is interesting to speculate whether the Lost Boys of J.M. Barrie's "Peter Pan" play and books fit into this category.