
Initially the best course of action is to carefully, and persistently, dig and hoe out all of the bindweed from your garden. Over the course of a few years, with almost weekly removal of the plant, the bindweed can be completely controlled, but new growths will eventually return.
The fastest period of growth for this weed is in the early spring months. This is the time to be extra-vigilant and dig out ALL of the new shoots as they appear. In this way, you can hope for a less troublesome summer, when your own plants flourish. The aim is to weaken the plant as much as possible - but you really do need to keep your eyes peeled for the slightest sign of the bindweed returning.
One thing to watch out for when manually removing the bindweed, is that it has extremely brittle stems, and this seems to be a "design feature" of this weed. If you are not careful, you can break the plant low down at the ground, leaving the root structure in place, and a new plant will quickly come back in its place. The only sure way to remove the plant this way, is to physically dig out the root structures, following them wherever they lead to.
If you are really suffering with a bindweed infestation, you should probably consider a chemical approach to removing the weed effectively. The use of a non selective weed killer, such as glyphosate, can be carefully applied to the broad leaves of the bindweed, being careful not to treat your wanted plants and the surrounding area. This weed killer is absorbed into the leaf and then is carried to the rest of the plant. This action is essential to kill the underground portions of the bindweed plant.
When spraying the plant, your aim should be to cover as much of the leaf surface as possible, and along the whole length of the weed, this way the weed killer is absorbed more quickly and in larger quantities into the plant.
Bindweed is a really nasty weed - good luck in eliminating it.