To tackle the shoots erupting near and beyond the walls I would treat each shoot as if it was an unwanted tree or sapling. Cut them down to about six inches, then with double-gloved hands paint the whole stem but especially the cut end with a 50/50 solution of SBK tree stump killer and water. Use a small brush, and a small container, and be sure to confine the solution to just the bamboo, not the soil. It is strong enough to prevent regrowth from felled trees, so I think it would have an effect on the remaining bamboo roots. I have used this method on large areas of nettles, brambles and wild raspberry, where tree roots prevent me digging, as well as on large tree stumps. I recommend using a small container and a small paintbrush in case of accidentally spilling the contents. I prefer this method to spraying, as it confines the solution to the unwanted plants. I did spray the nettles etc. with Roundup once, but it didn't kill the network of roots, and I didn't like the spraying. I would never plant bamboo myself, but a previous occupant planted one by the stream on my boundary. Many years ago we attempted to remove it and I thought we had succeeded but recently some has emerged and I will try the painting method on that. The only problem may be the smooth nature of the shoots, but it's worth a try. The bamboo looks so alien in such a natural situation.
Edited to add... I wrote the above thinking it would be a good way to treat anything that a digger couldn't reach, assuming that the bulk of the bamboo could be mechanically dug out.
I just read the original post again, @Fire and see that the garden is only 3m x 3m. Its not too large an area to try this method all over. It would need patience but might be preferable to using machinery, depending on circumstances. I tackled a larger area last year, in stages, ( not bamboo, but the tough weeds mentioned above, plus a thicket of aronia.) As each section of stems died back I cut them down to ground level to make it easier to move forward to treat more. It helps to paint any exposed surface roots too. A digger would of course have the benefit of removing the root system, but the stability of the walls would concern me I think.
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Cut them down to about six inches, then with double-gloved hands paint the whole stem but especially the cut end with a 50/50 solution of SBK tree stump killer and water. Use a small brush, and a small container, and be sure to confine the solution to just the bamboo, not the soil.
It is strong enough to prevent regrowth from felled trees, so I think it would have an effect on the remaining bamboo roots. I have used this method on large areas of nettles, brambles and wild raspberry, where tree roots prevent me digging, as well as on large tree stumps.
I recommend using a small container and a small paintbrush in case of accidentally spilling the contents.
I prefer this method to spraying, as it confines the solution to the unwanted plants. I did spray the nettles etc. with Roundup once, but it didn't kill the network of roots, and I didn't like the spraying.
I would never plant bamboo myself, but a previous occupant planted one by the stream on my boundary. Many years ago we attempted to remove it and I thought we had succeeded but recently some has emerged and I will try the painting method on that. The only problem may be the smooth nature of the shoots, but it's worth a try. The bamboo looks so alien in such a natural situation.
Edited to add...
I wrote the above thinking it would be a good way to treat anything that a digger couldn't reach, assuming that the bulk of the bamboo could be mechanically dug out.
I tackled a larger area last year, in stages, ( not bamboo, but the tough weeds mentioned above, plus a thicket of aronia.) As each section of stems died back I cut them down to ground level to make it easier to move forward to treat more.
It helps to paint any exposed surface roots too.
A digger would of course have the benefit of removing the root system, but the stability of the walls would concern me I think.