Roundup will kill bind weed. The fence line between my neighbour was full of it. I either shield other plants with pieces of cardboard or un-twine it and lay it where I can get to it. You need to spray it when it is growing strongly. Roundup travels down and kills the roots (nothing obvious happens for several weeks). It has taken me 3 years, it is nearly gone, just a few wisps left, but as I can't spray my neighbours garden, I guess I will have to spray those from time to time.
It is very difficult to dig it out, the roots go deep, and the slightest bit will re-grow.
I now have ground elder, which came in on a plant I was given, the Roundup will hopefully come to my rescue.
Good Luck.