I was asked to copy my answer from mythology.
In a nutshell: While it's still probable that Bram Stoker did not think of the "no reflection" feature, it's considered his invention.
Possible theory:
Back in the past, mirrors were made out of silver, and actually Balkan werewolves are considered a type of a vampire, so... if you add 2+2 u get 4. It's quite possible that the modern myth is a combination of the silver and soul reflection theories.
A full detailed explanation and references can be found in the full answer on Mythologyon Mythology.