I used to work for an insurance company that handled liability claims on this sort of thing. Just judging by the way we handled things, Walmart wouldn't be at fault for this. There is nothing they could have done to prevent it - and they even said they had hired exterminators in the past. It sounds like they took precautions against this sort of thing. This didn't happen because they were negligent - it was simply a wild animal that ended up in the wrong place. Walmart isn't at fault for that... it isn't one of their pets gone on a rampage or something.
I don't think she would win this lawsuit. The only one to blame is the bat. If somebody walked up and slapped me upside the head in a Walmart store, I wouldn't blame Walmart for it. They probably never knew a bat was even in there... All they'd have to do is show the receipts from the exterminator jobs to prove they weren't negligent...
I do not know if they would have to have insurance for animal bites... but I bet that even if they did, this would be denied because they still aren't at fault here. It's almost one of those things that fall under "act of God" where they just refuse to pay. My car insurance wouldn't pay if I wasn't the one at fault - the other person's would have to. I've never had homeowner claims, so I don't know how those work, it may be different, but... Just because they have insurance doesn't mean they HAVE to cough up...
Also, the article makes it sound like Walmart is refusing to pay, but I'd bet a third-party claims adjuster denied this and the walmart store itself (and its management) had no say at all. It does say management is very concerned about the girl, but I don't think Walmart itself had anything to do with denying this - JMO, from my own experiences... However, I have seen a store (not Walmart, but a store we covered at my employer) step in and offer services even AFTER a denial, particularly if it is privately owned and not a corporate location... but it is on their own wallets.
I could be wrong. I was never an adjuster or handled the claims myself, but I listened to many nearby adjusters' telephone conversations over the years...