<PERSON>, the creator of Batman, found inspiration in several sources, and it seems that he did not specifically set out to create a human, crime-fighting analogue to <PERSON>. However, one of his influences was <PERSON>.
<PERSON>’s initial idea was a superhero with bird wings. From Batman: The Complete History by <PERSON>, page 18:
When <PERSON> sat down at his drawing board in the Bronx, he immediately sketched in a figure similar to <PERSON>’s... Then he ... began experimenting with variations in the costume. He tried a pair of bird wings, perhaps inspired by an alien race in one of his favorite strips, <PERSON> <PERSON>.
Hawkmen from <PERSON>
<PERSON>
From Batman: The Complete History, page 144 (emphasis mine):
There has always been a subliminal association between vampires and <PERSON>; this was a hero who was designed to frighten his foes, and <PERSON> admitted that one of his inspirations was <PERSON> performance in the 1931 movie Dracula.
The Bat
Also, as <PERSON> points out in his answer, another inspiration for <PERSON> was the 1930 film The Bat Whispers. 167
That film is about a criminal called The Bat, who turns out to be an ordinary man, but the other characters in the story suspect at times that the <PERSON> is supernatural.
I wasn’t able to find a copy of The Bat Whispers online, but it was based on a 1920 play, The Bat, which was novelized in 1926. The novelization makes no mention of vampires or <PERSON>, but the characters do suggest that the <PERSON> is supernatural. A batlike, supernatural enemy lurking in the dark is reminiscent of vampires in much the same way that <PERSON> is, but this isn’t a direct reference to vampires. It does fit in nicely with <PERSON>’s stated desire to terrify superstitious criminals, however.
<PERSON> ornithopter
As mentioned in <PERSON> answer, another of <PERSON>’s inspirations was an ornithopter designed by <PERSON>. Someone flying this machine would be a sort of mechanical bat-man, with no particular association with vampires.
From Batman: The Complete History, pages 18 and 20:
From his boyhood reading, he [<PERSON>] recalled the ornithopter, a flying machine designed by <PERSON>. This device was essentially a glider, with wings built like those of a bat.
Picture from Wikipedia
Other influences
<PERSON> answer and Batman: The Complete History mention other inspirations including Zorro, but the influences above were the closest batlike or vampiric influences I could find for Batman. 167