That I can't say for sure, but the bird that the Romans thought was a type of cover for vampires was called the strix (the name for the screech-owl as well) and popular belief thought it suckled its young (Pliny for once is a bit dubious about this). It's possible that they were thinking of some sort of giant bat or a bat-bird hybrid, but I don't know enough about the later development of vampire myth to work out how it developed.

ETA: I also don't know the idea of vampires being old women transferred into them being our traditional vampire - I know a lot of it has to do with Bram Stoker, but the Greeks and Romans were also very wary of the ghosts of people who died young and who would come back (sometimes as demons, sometimes as werewolves).