Will a vinegar/soap/salt solution kill bindweed?
The short answer is 'no." The solution you're using--vinegar/soap/salt might kill a new small weed, or kill the top growth of a weed, but does not kill the roots. Field bindweed is a tough one to eradicate once it's gotten a foothold. Pulling it out doesn't work, because you won't be able to pull all the roots out, and new plants will come up from those. One thing you can do is cover the affected area with a weed barrier, eg. black plastic, and cover it with a thin layer of organic mulch to hold it in place. However, this will kill everything under it.
Chemical options include: Landscape areas: glyphosate (e.g., Roundup)