Born in the city of Grozny in the family of the artist. People's artist of the RSFSR (1985), laureate of Lenin Komsomol prize (1970). Member of the Union of artists of the RSFSR in 1966. In 1952-1957 he studied at the Palekh art school. Teachers - F. A. Yurtsev, A. V. Kotuhin, M. I. Shemarov, D. N. Butorin, A. V. Borunov. In 1957-1989, he worked at the Palekh art-production workshops. He was Chairman of the local Committee, the Executive Secretary of the Union of artists, Secretary of the party Bureau. Since 1993, directs the creative workshop "residents of Palekh". In 1977, awarded the Grand Gold medal of the international exhibition of the book in 1978 - awarded the Bulgarian order of Cyril and Methodius I degree.
Worked monumental (the Palace of arts in Ivanovo (1986), Palaces of pioneers in Ivanovo and Makhachkala boarding school in Anzhero-Sudzhensk, summer camp in Sugreeva), theatrical-decorative painting, along with his wife, K. V. Kukuljevic, book illustration ("Sadko" (1974), "Hello brothers!" (1978, cum them. Ivan Fedorov), the "Son of Russia" (1981), "Ruslan and Lyudmila" (1983), "the Life of Jesus Christ in the colors of Palekh" (1995)), writes icons. Themes of works: folklore, revolutionary, modern, ganarajya scenes, religious. Participated in exhibitions since 1958.
The Work Of B. N. Kukuliev are stored in museums: gmpi, timing, Voronezh OXM, OXM Ivanovskoye, GIM, GMAN, Pgaas, Kashin Museum of local lore, HF Russia.