There will be a rhizome connecting the stray shoot to the clump next door, you'll need to try digging the whole thing out back to the fenceline.
You also really need to insert a barrier under the fence, probably 3 feet deep, to stop this from happening again, because it will, this is what bamboos do.
Glyphosate can help, but it needs multiple applications.

This could be a potentially a chronic problem developing with a never ending battle for control for your property: either you or the bamboo.

Thanks for your help looks like a long job