Morning glory, bindweed, is a powerful survivor! It is hard to get rid of, herbicide resistant, yet pretty when it blooms and covers an ugly area, maybe your composter! But, it can tangle in your veggies, shade them out, use up soil nutrition. Studies show that due to its root system, field bindweed is a superior competitor for water under conditions of low soil moisture, and that corn plants growing with field bindweed were smaller and had lower yields.
Bless Master Gardeners! Laura B on Garden Web say here is the best non chemical way I know of to deal with morning glory/bindweed:
A master gardener here in Washington was able to help us understand why. It gets all its energy to survive the winter from its leaves. So this year’s leaves hold all the energy to survive and start producing leaves for next year. By removing the leaves to the plant as soon as they appear you will remove a link in the growth process. It takes patience and vigilance but can be done. Two years later my mother has completely eliminated all morning glory. I have passed this advice to anyone who needed it and it has proved sound over and over. The first summer is the hardest with the following spring much easier. The key is to get the leaves picked off. Don’t touch the roots as you’ll only end up spreading the problem. Leaves are the key link in the plants growth now and later. Good luck and yes it will seem like your only going two steps forward to have to take one step back. It can be done and there is light at the end of the tunnel. Although with a neighbor having it rampant in his/her yard can almost guarantee a constant source of misery for you. I can’t believe they even sell seeds for this noxious weed in stores. Good luck!
There is Laura’s solution and opinions! I think the Master Gardener must be right. But rather than remove leaves, a lot easier than digging deep for roots, I would do as the USDA article says, hoe every 14 days! You can’t get rid of the roots anyway. The taproots can be more than 10′ long, and other vertical roots even 30′ deep per the USDA! I know with some roots, breaking them off is just like pruning. The plant grows two from the break/cut point! Clearly, you wouldn’t want to use a rotor tiller – spreading and breaking up the roots into more sprouting pieces. Hopefully you never let it bloom and seed, or all those seeds, that last 20 to 50 years in the soil seed bank, will be dispersed as well! Either way, it will take two seasons. So do as makes you happy and stay with it. And, don’t put it in your compost! Prevention is a lot easier than postinvasion control. Word.