Oh Celia, I feel your pain with bindweed, OMG, that stuff is terrible! Some had been growing in a spot next to the house where it is shady and I hadn't installed any garden plants. Nearby, I had grown some Japanese morning glories, and didn't realize the bindweed had crept in among them. After that, the gardens suffered a couple of years of neglect, and during that time the bindweed exploded and took over 3 beds. Back when I still used chemicals, I had tried round up on it, and it only burns the leaves- they come right back. So for the last 2 years I have been diligent in pulling every sprout I see. That's really about all you can do, but eventually it does work. By the end of last summer, sprouts were less frequent, and very small and weak.
The roots of bindweed travel everywhere, and they're brittle, so each little piece that breaks off starts a new plant. I found it impossible to get the roots out. I read an article about bindweed that said you have to pull out sprouts every 2 weeks for 2 years to get a handle on it- and that sounds about right.
