In poetic use, bats are often associated with the coming of night and darkness. They have also a sinister association with vampires, notably in the tradition established by Bram Stoker in Dracula (1897). The bat is also taken as a type of blind creature, as in blind of Chancery.
have bats in the belfry be crazy or eccentric; the phrase is recorded from the early 20th century, and the colloquial use of ‘bats’ to mean mad derives from this.
like a bat out of hell (moving) extremely fast; recorded from the 1920s.