Taking up FloBear's suggestion, resist the temptation to zap the bindweed too early. Let it grow well up the cane. The roots of a well established plant can go down 10 metres in good soil conditions!! When you treat with glyphosate, it is drawn down into the root system by the plant, but the distance it travels depends on how much has been applied, so the more leafage you zap the better. Any root far enough down to have avoided the glyphosate will send up new shoots, and when they appear, do the same thing - leave them till you have a good surface area. After two or three applications the root will be exhausted.
I have been trying to eradicate Bear's Breeches - it has a massive fleshy root system. This is my third year of regular zapping it, and at last it seems to have given up. Just a few small leaves have appeared, and they have been zapped today.