Read, and follow, the label:
http://www.cdms.net/LDat/ld545000.pdf

Here is a link that might be useful: the label

Spraying your neighbors property without permission is illegal and could result in you paying very large dollars out as fines. It is not a good idea.
This product contains two of the most potent plant killers around and you should be wearing a very expensive respiratory protection mask as well as full protective clothing. This product is not an environmentally friendly material.

"Would it be ethical for me to spray a foot wide strip on her side of the fence to keep the encroachment to a more manageable level?" Unethical and illegal.

"What would you say if a neighbor did that to your side of the fence?" I've lived next to a 'whatever' property/shared fence for years. Mow/weedwack your side and move on.

"Naturally, I would not spray anything that would be considered a flower or a desirable plant...just the cheat grass and purslane and the like." Your definition of a desirable plant may or may not match your neighbors'. Some people have better things to do than manicure a fence constantly, or attempt to foster a monoculture of grass in a mowed area. A few cuts per year should keep woody entities from taking hold.

Have you talked to your neighbor about this? If tidiness is out of reach along that stretch, how about just going with it, put some wild (non woody) vines on the fence and just enjoy the show.

Bare earth erodes. Mulch may be more useful than so much spraying.

A pic might help you find an idea/solution you like if you don't like my live'n'let live suggestions.

Don't spray it on frozen ground--you are likely to have it "travel" when any rain or snow melts and moves it elsewhere. You may need to experiment/gain experience to see how close you can get to things you want, but if their roots go through a treated area, they may still suffer ill effects--and you won't know how close is too close until you damage something you want.

Thanks all for your suggestions. I already knew what you would say about spraying my neighbors side of the fence...but was hoping that some of you might have a thought like mine....drop a swimming pool of weedkiller on her side of the fence. (Just kidding) Yes, you guys are right. It wouldn't be very nice of me and she is definitely the type of neighbor who would press charges against me if she knew I sprayed her side with "GOD AWFUL DEMON CHEMICALS!" I'm trying a different approach. I scattered some wild-flower seeds on her side, in and among the grassy weeds. That way, her weeds won't bother me as much, and she will think her "let-nature-reign" approach is working, as evidenced by all the pretty flowers that just mysteriously popped up on their own.

Side note: I told her one day that I was planning on putting in a bee-hive and she went ballistic. "I hate bee's!" she said, even tho she's a self professed nature-person. Judging by her reaction I decided that maybe a bee-hive would cause problems so didn't put one in. Wouldn't you know, later in the summer she rang my door bell to announce that one of "my" bees stung her. Good gravy, now I knew I was in trouble! From this day forward, every wild bee in a 10 mile perimeter would hence forth be my responsibility when on her side of the fence! Secretly I hoped she was allergic...but no such luck. (incidentally, the bee she was stung by, according to her description was a wasp, not a honey-bee...proving even further that it couldn't possibly have been one of "my" bees.)

Thanks beeone, I will wait until spring to spray my areas.