As revealed by Professor Cornelius McCobb, Bombie is not actually dead. Like all “real” zombies, he was a poor man who was bewitched, in Bombie's case by the vengeful African voodoo doctor Foola Zoola, to become his mindless slave. The enchantment also gave Bombie a greatly-expanded lifetime and superhuman strength and resistance to cold, drowning and starving. Still according to Professor McCobb, Bombie is still conscious the whole time, but is unable to reflect that through actions, and can only act following Foola Zoola's orders.
The vengeful Foola Zoola sent Bombie after a young Scrooge McDuck to give him a bewitched voodoo doll, which would put a curse on Scrooge, reducing him to the size of a mouse (which is Foola Zoola's favourite spell). However, at the time, Scrooge's suit made him look more like his not-yet-born nephew Donald Duck than like himself in his usual attire; Bombie, because of his voodoo-induced mindlessness, was therefore unable to recognize Scrooge when he caught him, as Scrooge had reverted to his usual self at that point. Nonetheless, a curse Foola had put on Bombie made him stalk Scrooge, whose presence he could sense in spite of his inability to recognize him. The poor duck was chased all around the world by Bombie for years, until he managed to get another voodoo doctor to put a counter-curse on Bombie, which froze him into place for decades.
Bombie made his first appearance in this 1949 story. It opens as Bombie, who has recently been revived as the counter-curse wore off, arrives in Duckburg, still looking for Scrooge McDuck. Bombie runs into Donald Duck, and thinks he recognizes in him the young Scrooge he has been looking for for forty years, and gives him the doll, which stings Donald. Learning Bombie's backstory from Scrooge, Donald leaves for Africa along with Huey, Dewey, and Louie. As he no longer has a mission to fulfill, Bombie is confused, and tears begin to pour from the old ghoul's pupilless eyes. Whereas Donald is unsympathetic to Bombie, the kids take him into pity and decide to bring him back to Africa with them. Donald eventually uses him as a weapon to get rid of Foola Zoola's voodoo tribe by tying rubber to his feet and sending him bounce around in the village, as the massive zombie knocks down soldier after soldier in his endless bouncings. He is last seen still bouncing by the ducks as they leave Africa, and they comment that even if he bounces for months he'll still be alright, and saying that hopefully, Foola's curse will end one day, and Bombie will be free.
Bombie the Zombie is prominently seen in episode eleven, which reveals more details about Scrooge and Bombie's backstory.
Bombie the Zombie makes a cameo in the banquet scene at the end of this adventure, in Duckburg. This has sometimes been taken as a hopeful hint that Zoola's curse did wear off, allowing Bombie to come back to his Duckburg friends.