www.rhs.org.uk/Plants/12869/Phyllostachys-nigra/Details
This is the stuff. Clearly we had the right kind of soil and sunlight in London for the stuff to take off.
It was fairly confined where it was planted but after about 3 years it suddenly seemed to go mad with shoots appearing 3 feet away. It seems to lurk underground all year and then it would grow 10 inches a day in May topping out around 7ft and then stopping for another year when a new shoot or 10 would appear. I dread to think what it could do in a large garden if just planted out.
For context the link above also calls it clumping in 2.5 to 4 metres.... Obviously I'm conditioned by tiny London gardens but that's a sodding great big clump if it's 4 metres in diameter.
Cultivation
Grow in fertile, humus-rich, moist but well-drained soil, in full sun or partial shade. Protect from cold drying winds. In a container grow in a loam-based compost and feed with a balanced liquid fertiliser on a monthly basis during the growing season. May remain clump-forming in poor or dry soils but can become invasive in warm, moist or favourable conditions.
It did make the most fantastic swishing noise in the wind though, v relaxing like being by the sea. Constant sweeping of the leaves though even though it was evergreen they are constantly regenerating.
OP, if you google contemporary fencing you will get some nice ideas for both horizontal and vertical fencing particularly the slated kind which have an open appearance.
Problem is, it doesn't sound like your neighbour has either the means or the inclination to put up a proper fence.
With small children I would be really unhappy with a wire fence. I think the first step is to say that you are really not happy with it as it stands and you want some sort of fencing reinstated.
The alternative is also to speak to a half decent local garden centre. Some of them will send a garden designer out free of charge to do a consult. They will put a plan together for you and a list of plants which you will hopefully buy from them.