Is there anything I can do to stop it? Can I ask them to do something? I don’t want my hard work to go down the drain with the long term disaster that is the field bindweed.
Field bindweed, Convolvulus arvensis, is indeed a nuscience for home gardeners, farmers, conservation authorities, parks and cities alike. It is a perennial that can spread by an extensive rhizome network underground or by seed dispersal from pink or white flowers. Its climbing stalks/tendrils grow at a rapid rate and entangle anything they encounter including cultivating & harvesting equipment.
That being said, in the home garden scenario, creating an underground barrier along your fence line with the offending neighbouring property may give you some relief.
Also, any bindweed plants on your side of the barrier can be cut off at soil surface level and disposed of in your garbage (not into your composter or the city garden waste). Be vigilant, this cutting must be done before any new plants get to the 3 leaf stage as the idea with this method is to not disturb the soil but to starve the plant roots of sunlight and energy for growth.
Soil disturbance will only divide and spread rhizomes so head out with your scissors and cut, cut, cut. You will find the number of plants diminishes over time but true eradication is rare as seeds will be deposited by birds etc…
Keep at it and you’ll accomplish a level of control you can live with.
Hope this helps.