Abandoned shortly after birth with no known family or home, Bumbum begins life discarded and alone, forced to navigate a hostile world. His story opens with a near-drowning in a river, underscoring his extreme vulnerability and lack of survival skills. Following this trauma, he encounters Nora (sometimes called Big), an older, experienced stray dog who becomes his primary mentor. Under Nora's guidance, Bumbum gradually learns essential tactics: foraging for food, evading dangers like dog catchers, and understanding urban environments like sewers and streets. This mentorship defines his coming-of-age journey from helplessness toward cautious independence.

In the television series, persistent rumors that his mother might be alive drive Bumbum's primary motivation, fueling a relentless search across various locations. This quest shapes the narrative of many episodes, often reflected in their titles. During his travels, companions Nora and another dog, Bunta, join him. Their journey faces complications from antagonistic humans, notably a cruel dog breeder who seeks to capture Bumbum. The breeder aims to train him as a fighting dog, believing he possesses suitable physical or temperamental traits for violence. This threat forces Bumbum into direct confrontation with human cruelty, reinforcing themes of resilience.

The theatrical movie presents an alternative story. Similarly abandoned as a young puppy, this Bumbum lacks any knowledge of or drive to find his parentage. Instead of a focused quest, the film depicts his episodic experiences alongside older strays within vast sewer systems. These include evading dog catchers, brief participation in dog fights, and philosophical discussions about life and survival. His characterization here emphasizes naivete and obliviousness to danger, leading to recurring comedic situations where his innocence frustrates more world-weary companions. The film concludes on a lighter note, showing him playfully chasing butterflies, symbolizing unburdened childhood joy.

Across both media, Bumbum retains consistent traits. He possesses wide, expressive eyes conveying innocence and exhibits a blend of animalistic behaviors (like scavenging) with occasional anthropomorphic mannerisms such as standing on hind legs or crossing his forelegs. His repetitive name reflects his youthful, simplistic identity. Key relationships beyond mentor Nora include companion Bunta and sporadic interactions with other strays offering diverse perspectives on independence versus dependence on humans. His development remains rooted in adapting to an environment where kindness is scarce and trust requires constant negotiation.