My chickens seem to help control the bindweed as well. They don't eliminate the bindweed altogether, but seem effective at reducing its vigor.
We have a 50x50 foot deep mulched chicken run with fruit trees. Right outside the chicken run (our garden area, also deep mulched), the bindweed is deep green and scary aggressive. Inside the chicken run, the bindweed almost seems anemic. Doesn't seem like something at all to fear. There's a clear delineation of this effect right up to the fence line.
I'm not sure why this is. I don't get the sense that the chickens eat the bindweed. We don't see them nibbling at it. I was wondering if it has to do with the chicken manure. If so, that seems pretty mild, as we only have 4 chickens roaming 2500 sq feet, and the effect of their manure is buffered by 12 inches of wood chip deep mulch.
We also have 7 ducks, so later in the summer once the garden gets established, I want to see if I can introduce the ducks to manage the bindweed on the other side of the fence.
If we're able to use poultry to manage our bindweed at "anemic, non-aggressive levels," that would be quite a win.