To be honest, bindweed doesn't bother me that much. It's easy to spot and to pull out to the ground level at least. It dies back in the winter, so you don't have to keep fighting the battle then too. It also grows fairly individually, not in big clumps like couch grass. If I could only choose to remove couch grass or bindweed from my plot, I'd take out the couch grass.

Oh, and I do try and take out all the bits I can, but I'm not chasing down more than a fork's length to get them!