HELP! Bamboo - has anyone had any success with using white vinegar to kill roots?

I'm trying to eradicate some bamboo which is coming up on either side of a garden fence, i.e. in 2 separate gardens. Neither owner knows where it has come from, and it seems to have appeared fairly recently. It is coming up in thin individual stems, not clusters. I dug down to about 18 inches around one stem and still cannot see the origin of the roots; i.e. there's no rhizome, just a smooth stem disappearing into the bowels of the earth, with a slight sideways tendency. From this I deduce that it's a running variety, not a clumping variety. (The bamboo I've dealt with in the past had easily-dug rhizomes close to the surface. No sign of that here.)
I've abandoned the idea of digging it up, as it will be hugely disruptive to surrounding shrubs, and the chances of getting all the roots out seem slim.
My thought was to try the natural remedy of pouring neat white vinegar on the roots (having first dug down to 6-12 inches to minimise contamination of the surrounding soil. If that fails, I will opt for glyphosate
My question is: has anyone tried the vinegar method, was it successful, and can anyone suggest a better approach than what I've described here?
Huge thanks in advance for any help/advice/encouragement!
I've abandoned the idea of digging it up, as it will be hugely disruptive to surrounding shrubs, and the chances of getting all the roots out seem slim.
My thought was to try the natural remedy of pouring neat white vinegar on the roots (having first dug down to 6-12 inches to minimise contamination of the surrounding soil. If that fails, I will opt for glyphosate

My question is: has anyone tried the vinegar method, was it successful, and can anyone suggest a better approach than what I've described here?
Huge thanks in advance for any help/advice/encouragement!
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Think of running bamboo as couch grass on steroids. You need to dig out every bit of root to stop it coming back. You could try digging down along your own fence line and installing a root barrier but I suspect it will be hard work and expensive.
Glyphosate needs to be applied to green growth in order to be taken down to the roots and you may need several applications. You need to protect surrounding plants or it will kill them too.
I agree with @Obelixx … I’d use the glyphosate … following the instructions on the pack.
No.