do you have a hospital/qt tank? try separating her into that, and acclimate her using part of the water from your tank and some fresh treated water. you can add a tiny bit of aquarium salt, as well as bettafix [basically watered down melafix, so it's not too strong for them] to see if that perks her up.
she might just be stressed -- in my experience tetras and bettas aren't that great a combination, but usually that's for males.
just try the qt/hospital tank. if you don't have one, you can probably get a critter keeper at your local pet store for a few bucks. up here in canada they're like, $6