I was generalising bats overall, worldwide due to the lack of bloodsuckers outside of the Americas.
Actually, it DOES. Majority of bad press comes from the late part of, or after the game era.
They seem to have largely been considered a nocturnal, flocking, squeaky, flying mouse. The fact that they have live young, rather than lay eggs like proper birds, appears to be noted and thought significant. http://bestiary.ca/beasts/beast250.htm
I think that, because they were nocturnal, they were likely often associated with the supernatural --- in much the same way that other nocturnal animals, like cats and owls, were. Which does not necessarily mean bats are considered a bad thing, but probably bats would be considered a weird thing.
Certainly vampirism and bats is a Victorian myth, rather than a medieval one.
We used to get bats in my house all the time as a kid, at least until we replaced our old windows. We'd generally try to catch them alive with a butterfly net and release them outside. The thing is once you get a hold of one and get a good look at it (trust me use gloves little needle teeth) they are unbelievably cute little critters. I'd have no problem thinking an intelligent bat that knew enough to act like a domesticated pet would be able to easily make friends. Of course a mythic bat might not have the personality for it (I could see shy as a reasonable personality trait for a bat) but IMOHO they'd have the looks.
As far as I'm concerned a infernal bat might drink blood just like an infernal cat or toad or raven might. But thats just a coincidence. A bat "magic" aligned with another realm almost certainly wouldn't drink blood though. How common say a bat of virtue is and what sort of abilities it might have is another issue entirely.