Unfortunately, once a yard is infested with bindweed there is not a quick and easy solution to eliminate it. 

Seeds can live in the soil up to 20 years and it has a very deep root system that continues to store energy and put up shoots, even when you mow, hand pull, or spray the greenery above the soil. The roots are so deep that is it not realistic to dig the plants out. 

Here are some management techniques you can start implementing now that can keep the problem from becoming worse and will diminish the bindweed over time. With bindweed it not a question of elimination, but of management. 

1. Don't let the flowers go to seed. Pull, mow or spray to prevent seed heads forming.

2. Remove the foliage above the soil so that the plants don't continue to photosynthesize and send energy to the root system. (Remember that the root system already has plenty of energy, so even when you pull, mow, or spray the tops, you will continue to have new shoots. You will need to remove foliage consistently over the course of years. If you choose to spray an herbicide, it will require multiple applications.)

3. If removal is too labor intensive, you can use black plastic, cardboard, newspaper, etc. to shade and smother the plants. 

4. You can try to outcompete the bind weed by overplanting a taller plant that will shade it out, such as tall grasses. Continue to pull the bind weed that emerges however. 

5. If you want to use the area for growing food or other plants, consider using raised beds. 

Here is information from our CSU Extension agency with more detailed information about bindweed management: https://planttalk.colostate.edu/topics/weeds-cultural-problems/2104-controlling-bindweed/