Bindweed, assuming you are referring to Convolvulus arvensis, is one of the many species of plants that have developed resistance to glyphosate (Roundup) in recent years. It used to be possible to control bindweed by spraying it with Roundup in the fall, but that probably won't work now. Bindweed was naturally able to survive spring and summer applications of Roundup even before the development of Roundup Ready corn and soybeans. Once Roundup started being applied to crops on a large scale, bindweed quickly developed complete resistance.
2,4-D will make the leaves curl up and turn brown, but it won't kill the plant. In spite of its very common use as a dandelion killer, 2,4-D is basically useless against most perennial weeds. It may kill the top of a plant, but doesn't stop them from resprouting. Mostly, what 2,4-D is "good" for is damaging or killing non-target species like tomatoes and grapes.
Picloram (Tordon) will kill bindweed. It doesn't kill irises, but it does distort their growth for a year to two after application. However, picloram is also both persistent and highly mobile in soils. Consequently, it should be used only with great care.
Pulling or hoeing bindweed can work, but requires incredible persistence and you have to be vigilant about removing it immediately when it re-emerges.
The simplest way to get rid of bindweed is to plant something that grows tall and has an aggressive root system to out compete it. Big bluestem and indiangrass are my favorites for this purpose, but any tall rhizomatous grass should work. Of course, you have to be able to tolerate tall grass growing in that area, which may or may not be acceptable, and it requires patience since it will take four or five years to get rid of the bindweed.
