Noxious weeds are found in every state, and Bindweed is one in my state. I tried to fight it organically for years. I did the thing that AlexinSD is considering. A few years later, when that failed, I dug up to my knees many areas, gently following all those runners and removing, not pulling them. That made a difference, but the vacant lot next door seeds and blows the stuff back in.
I have a bottle of Roundup that is on it's third summer in my shed next to my tools for weeding. It only comes off the shelf for bindweed and blackberry, from the vacant lot adjoining me, and without it or something much worse, it would be rampant in my yard.
