Your local govt may have an option for you. Just like a neighbor/
property owner can't divert runoff water/drainage onto your property,
infringing on your property or its normal use, some invasive non-
native plant species, that a neighbor has purposefully planted, have
to be controled by that neighbor from invading your property.

You will need to consult with the local govt and applicable ordinances
and with the neighbor. An applicable ordinance may not specify a
particular specie or scenario, but is applicable enough to cover an
unforseen circumstance as with this bamboo. The neighbor, not you, may
be required to install some sort of petition at the fence line or
control the spread from on his side of the fence, but if you are able
to work with the neighbor, the overall outcome (including civil peace
with your neighbor) may be better resolved for both of you.

If an ordinance is found to be applicable, the neighbor may be
required to perform any removal from your property, if the bamboo does
eventually invade your property. It would be good for you to somehow
demonstrate what damage can be expected and/or what hardship the
invasion would present to you and your property, also, in your effort
to site the ordinance and have it enforced on your behalf. If there
is some sort of damage and/or hardship being demonstrated on his own
property, for he, himself, this can be further evidence for your
concern about it invading your property, i.e., example: is the bamboo
growing toward his house/other structure/etc., also, such that he is
having to take measures to control that direction of his own invasion
scenario?

Now is the time to best address the issue, as you seem to be doing,
not after the bamboo has established itself on your property.

Sonny