It's a long, boring process! You have to pull up every plant, making sure that you not only get the tops, but the entire root system as well. If you get rid of it all, it should not come back.
Roundup or similar systemic killers is the only sure way. It will take you a couple of seasons and a lot of anger. Pulling it up will fail as you need to get 100% of it, anything left in the soil in the way of root will grow up again. We've been using Roundup for most of this year and the problem has reduced but not gone away, I figure a bit more will sort it.
I pushed bamboo canes into the ground and let the bindweed grow up it, then simply painted the whole cane with weedkiller.No damage to the surrounding plants and took great satisfaction in watching the weed shrivel up on the canes.Success, HURRAY!!!