Early in Spring, I found a bindweed plant in my front gravel garden, near the hedge. Using a tip from the late, great Geoff Hamilton, I inserted a cane close to the plant and tied it onto it.
Donning plastic gloves, I rubbed the plant throughly with glyphosate based weedkiller stick, then removing gloves. I carefully wrapped plastic around it to protect any plants that might touch it as they grew.
Now, it appears well and truly dead after sweating all summer long inside it plastic tent and should be fine to remove: