I think it is strange that her fence is shy of the property line by 1 ft. You are saying if I understand right that 1 ft of the yard on 'your' side of the fence, is her yard? So not only is the fence entirely hers, but another foot on your side is hers? I don't think it would cost you anything to initially consult an attorney or at the least I would call city hall and find out what the laws are for fencing in your town/state. If that other foot IS hers then she is responsible for its upkeep. Or can decide to be at any time. It also means you cannot paint the fence or hang anything on it, or grow anything that would vine or touch it-as she can cut that off. So the question then is, what happens to the 'no man's land' space? If you put up fence ON the property line, then she may be responsible for her side of that. It wouldn't matter if she had a row of fence of her own anywhere else on her property. So you would basically have 2 rows of fence, 1 ft apart. If both rows were privacy fence, I don't think there would be enough light for any weeds to really live there. Besides that part would be hers. Then you could paint your fence, hang things on it, grow whatever you want on it, as long as it doesn't grow over the fence onto her side. Round up does make products that suppress plant growth for an extended time. These are popular for gravel paths, driveways or sidewalks and nothing will grow in the area for several months after application. If she is not wanting anything growing along the fence and your bush is dying, I think it is safe to assume she is using that sort of product. You may want to dig down along your line and place a layer of contractor grade plastic as a barrier between her soil and yours so that this product will not leach into your soil. Or you could as you noted, make a raised bed and I would still line that back area with the plastic. If you are planting shrubs that root down very far they will have access to that soil. Shallower plants and raised beds with plastic between the soil areas will more than likely fix your problem. There is of course the possibility that she is spraying your plants w poison on purpose when you are not home because she does not want them growing there. If that is the case, you have no choice but to 1. move 2. plant your things in another area of the yard altogether or 3. catch her on camera.
