The actions of Vampire Batman are heavily inspired and influenced by Bram Stoker's Dracula (1992). In particular, his shadow moves independently of his body, he climbs the outer walls of the space station much like Dracula climbed the castle walls, and he turns in a horde of rats just like Dracula.
The opening segment, where Batman and Robin meet Catwoman dressed in "Tarzan" styled costumes was inspired by the story "The Jungle Cat-Queen" which appeared in Detective Comics #211.