Naugler was born in 1948 in Lunenburg County, Nova Scotia. Today, he still lives in Lunenburg County with his family. His brothers, Leo and Ransford, are also visual artists. As long as he remembers, Bradford and his brothers made all their own toys, such as skis and sleds, out of wood. At age 14, Naugler quit school to work full time with his father in the woods. He worked as a woodsman, also trapping bear; later, he worked as a garage mechanic, house painter, and labourer.
In 1989, Naugler began carving with a chainsaw and painting his creations. He did not go to art school or draw inspiration from art history or art galleries; rather, he looked to the woods and the animals around him. He was influenced not by other artists, but by his rural environment, his intimate knowledge of the woods, and the comfort he drew from his surroundings. These fuelled his creative impulse. "I get a lot of thoughts in the woods," he has said, "It's a world of your own....I might see a deer or another animal. I make sculptures that come from memories of these moments." His subjects for carving include animals such as roosters, bears, bobcats, fox, and fish, as well as human figures, both small and life-size. His works often show a sense of irony and humour.