I used to battle bindweed every summer here in California, until I saw that any solid grass cover would inhibit the growth, so always keep a grass cover on the ground. Bindweed needs disturbed or bare soil to grow, and their seeds may remain viable for 100s of years, so any time in the future you create bare soil, you can awaken those dormant seeds and have a new infestation.

I do not know what country you are working in, but I would choose a local annual native grass first, then a local perennial native grass seconds, and perhaps a local native legume species to provide the inhibiting cover that you need.