I am clearing an area of my garden over the past few weekends and I'm
digging as much of the root out as I can find. Bindweed has a long white
brittle root system, so you have to dig carefully using a trowel. (The
intention is to weaken the plant, however it may be a fools errant as the
roots can go down 20 feet). Unlucky for me the neighbours keep growing a new
crop so I'm destined to struggle with this weed. I keep niggling it with a
hoe its not really a problem keeping this, and other weeds down.

If you search google groups for Judith Lea's method, which is basically to
stuff as much of the bindweed into the plastic bags (the small ones for
sandwiches) as you can, the more the better, slosh a little roundup
(diluted) into the bag, seal with a twist and leave it alone. The stuff
will work its way though the foliage and right through to the roots....