Anyone who thinks you can “control” a running bamboo in the USA is delusional. I had a neighbor who planted it and the struggle to keep it from overtaking my rose garden, my fruit trees, my lawn in general became the bane of my existence. I finally dug up the roses and sold the house.
The neighbor is right, mowing it only leaves behind sharp stubs that will cut you to pieces (I’ve had them pierce the soles of my shoes). Then the bamboo regrows from each stub. Each plant sends out runners for 10 or 12 feet, with new plants at regular nodes along the runner. There are no natural enemies, no restraints, no disease - its like kudzo and japanese beetles - it should not be planted in a yard.
The runners will break through brick walls, concrete block walls, tear up driveways, damage house foundations. You can “contain” it in certain plastics, but those plastics are very expensive and even then you must be vigilent.
I only know one substance and one method of application that will kill it and that is also likely to kill any surrounding plant life.
In many states bamboo is listed as a noxious weed. In this case, I’m with the neighbor.
The fact that the neighbors are whining about birds chirping and not about bamboo growing through retaining walls, foundations or driveways indicates this is not the noxious variety here.
If the neighborhood nazis can make her cut down 30 year old bamboo due to birds chirping or other such trivial reasons, then they can make you cut down a prize oak tree because it is casting shade or dropping leaves in a neighboring yard.