There are basically two types of bindweed, hedge bindweed which is a climbing variety, and field bindweed which is a ground covering variety.
They spread by root or rhizomes, but field bindweed is mainly spread by seed.
Preventing field bindweed flowering will prevent seed set.
Both are difficult to control because they both tend to swamp adjacent plants making eradication difficult without damaging the said plants.
The rhizomous roots are usually white and brittle and, if broken, are able to regenerate from the smallest of sections.
The roots can pentrate a few metres deep into the soil making them difficult to remove completely.
One method of control is to spray the weed when it is in active growth with a glyphosate based weed killer.
However this in itself can create a problem in that the chemical is not selective, and will also damage or kill adjacent plants if it gets onto their foliage.
One can try and isolate the clumps of weed by means of cardboard / glass/ plastic screens placed strategically to protect garden plants from over-spray.
There are paint on applicators on the market which are possibly OK with small infestations.
Digging them up is the best option but this relies on finding and removing every bit of the root system.
Any missed or broken pieces of root will and re-grow.
Constant hoeing will help to weaken the plants to a point where they may die off.