Problem with bindweed is that the root is so extensive that when you pull one out, you break off several pieces that get left in the soil, and each of those pieces then starts to grow - vigorously. You need to carefully dig back to the root source and pull out the whole thing to end the cycle, and pray that new seeds don't blow in with the next storm.
While I hate to use chemicals, I find the only solution to bindweed is to rip off most of the top growth and immediately spray that fresh cut area with glyphosphate and leave it. Within a few weeks the whole plant and all bits of root will be dead. It's taken me a few years from masses of bindweed and now I have only the odd belligerent piece trying to grow.