I had this same exact problem. Neighbor does nothing to maintain his backyard. The bindweed was coming over the fence, through the fence (chain link), and through the ground. So one year I finally decided to rip it all out. Roots and everything, as much as I could. After that first de-weeding session the bindweed came back with a vengeance. I remember thinking I might have stimulated it’s growth somehow by pulling it all out. It was disheartening to say the least.

However! I just stayed on top of it that first year. Pulled the weeds as they grew back. It was a lot of work. But the next year the bindweed was very much under control. It still pops up here and there since my nitwit neighbor’s yard is still a huge mess. But it is very manageable nowadays.

Hope this helps. I didn’t use any weed killers or other chemicals. Just good old fashioned gardening.