I nearly gave up my allotment after the first year and a half due to bindweed but one of my neighbours a few years ago said that if you dig out as much as you can and keep hoeing any new shoots that come up, it will be gone in two years. He was almost right. If you can just keep on weeding the bindweed so that they do not see the sun, they weaken after two years and practically give up. It is much more managable now. Good luck