Four ways to kill off bindweed
Snip off weed at base
Once you have identified the plant (whose thick white roots run deep and also run horizontally, growing stems and leaves where they surface), see how much of it there is. If you just have a small patch, remove the top growth weekly to weaken and eventually kill the plants. Cut the bindweed at the base with scissors or shears, which will force it to use up its energy reserves in its roots, which will eventually kill it - but you have to regularly. Spray it Use a spot weedkiller, preferably a systemic type - glyphosate - which the plants’ leaves will absorb and take down to the roots, killing the whole thing. For maximum effect, do this in early summer when the bindweed is in full growth. Place bamboo canes where you see it to allow it to wind up them, so you can paint the weedkiller on the leaves for best effect.
Pour boiling water over it
If you don’t want to use weedkiller, pour boiling water over the bindweed and around three inches beyond where it is growing, to kill as much root as possible. You may have to do this regularly until there is no sign of it.
Dig up affected plants
If your plants are engulfed in a mass of bindweed, you’ll have to dig up those you want to save and untangle them from the weeds, making sure you remove any traces of weed roots growing among the roots of the plants themselves, and temporarily pot the plants in compost. Wait several weeks until the weeds are growing strongly, then spray with glyphosate. After a few weeks, all the weeds should have died.