BOLLYWOOD is the informal name given to Mumbai-based movies and music coming from India. Other areas of Indian Cinema have other informal names.
What makes "it" a Bollywood dance? It's simply a combination of dance movements from various genres - Indian or other world-genres - choreographed to music from the Hindi-language films.
In order to effectively teach Bollywood Dance, an instructor should have proper training in various styles of dance - Indian Classical being foundational, folk dances of India, and other mainstream world-dances such as jazz, hip hop, modern etc are very beneficial.