Several websites offer suggestions for the removal of bindweed. The most extreme suggestion was simply to move away. The vigorous growth and nefarious root system makes it near impossible to eradicate. The University of California Extension says, "bindweed is one of the most persistent and difficult-to-control weeds in landscapes and agricultural crops." They suggest cultivating (i.e., pulling) it every 2-3 weeks to prevent germination. Other sites similarly recommend frequent pulling, claiming this will eventually "exhaust the roots." I don't know if this is accurate, but it sounds good to me, so that's what I have been doing for the last month.
The bindweed is mostly confined to the backyard, and specifically, only the north half, which is far sunnier, and separated from the south by a sidewalk. I have spent about 20 minutes in the morning, and another at night, scouring the yard for the telltale diamond-shaped leaves and/or viny appearance. Almost every site I found simply said to pull the weed, with no indication of trying to dig it out. However, after 2 weeks of picking about 75 bindweed plants per day, I dug one up and discovered the size of the root/rhizome--it's huge, as shown above. The UC site claims a plant can spread 10 feet from its root system. I switched my simple pulling to digging out as much as I can of each plant. Once you know what to look for, they are very easy to spot in a hunk of upturned dirt--they are thick, white, and make weird 90-180 degree turns, which can make them difficult to simply pull out of the soil without breaking off.
So far I haven't seen a significant decline in the number of bindweed found per day, but I can only assume it will eventually start working. The graph below (May 12-June 5; update on June 26 is below) shows the number of bindweed that I picked/dug up per day. The decline in the last few days could be a number of different factors--perhaps my hard work is paying off, perhaps I didn't spot as many as I should have, or the cooler nights might be inhibiting their growth (the last several nights have been in the high 50s, compared to nights in the upper 60s & low 70s for the previous few weeks).
Update: June 27, 2018 (3 weeks later)
Update: July 26, 2018 (7 weeks from the original post)
July in Indianapolis this year was very hot and dry. The various cover plants in my yard started to shrivel and I had larger patches of dirt. My twice-daily bindweed digs have significantly decreased, from the 50s at the beginning of July, to the 20s by the end of July. However, I have no way of proving it is the digs, or simply the dry heat, or even just a natural decrease for this time of year. I have caught each plant before they reach 6", mostly before 3", and no plants have flowered. I think I have increased my proficiency at digging out the white, fleshy rhizomes, although sometimes they are too deep to find efficiently, especially in the grassy areas. One artifact in the data, is that I realized I have been digging up 2 types of bindweed--field and hedge. The former has lighter colored and smaller leaves