getting rid of the stuff will require time and persistence because of the persistent and extensive root system -- plan on a minimum of several years.

There are many reports that wild Morning Glory is resistant to the glyphosate "weed" killers, so they are probably not the best method of control.
Covering the above ground parts of this plant can, over time, cause the roots to eventually die providing new growth does not get access to sunlight. Plastic, made from non renewable resources is not the best material to use to suppress any plant growth. In addition plastic will stop air exchange in the soil and can cause that soil to become anaerobic.
The same mechanism in the plant that stops the movement of the "weed" killer will also be at work if a leaf is put in a jar of the stuff. Diluting the poison only serves to allow the plant to develop immunities faster.

Roundup and its generics work well on this stuff. But it's still a battle. I've 100% killed patches only to find it's back the following year, apparently from seeds that dropped. Pulling it out is a total waste of time - it has a root system like a hairnet.

Roundup works on it only if you can spray the whole plant...which is hard to do when it's intermingled with lawn and around desirable plants. If you just spray the crown, it will only damage the plant; not kill it. (adage applies: what doesn't kill it, makes it stronger.) If you grab all the vines and pull them all into a strip, and spray that strip, making sure every leaf is dripping wet; it works. But who can do all this when you have 50 million of them growing everywhere.

I prefer to use Weed-B-Gone, as it works too, but you have to use the same idea. You can't just spray the crown, you have to spray down the vines and all over the leaves. At least weed-b-gone doesn't kill the lawn grass, tho.

(ps under no circumstances, let it go to seed. Each seed is incredibly viable. The only redeeming quality the plant has is its cute, little flowers....but you must force yourself to keep them plucked off.)

Frippin' bindweed seeds remain viable for 20 years or more, so, NO FLOWERS as runswithscissors (a fun moniker, albeit somewhat masochistic) says.

And, like bstnh1 says, Pulling it IS a waste of time.

The bottom line: TENACITY. Ya gotta stay on it for a couple or three years, glyphosate or Weed B Gon or whatever - ya gotta stay on it! Every little re-growing spot or germination. Bindweed = obsessive-compulsive tenacity!

It took me 4 years to get it eliminated from my yard, but several years later it still remains absent.

O/C hortster

I have eliminated Bindweed from several planting beds without spending any money on plant poisons simply by removing any and all roots and plant bits and pieces. That did not take me 4 years of trying either.

You did that on an acre and a half, Kim?

I did, but not in one day, or week, or month. Now if I could train the birds to not eat the seeds of Sheep Sorrel, Creeping Charlie, Henbit, etc. life would be much easier.