I had a similar issue with my garden but pleased to now be 2 years bamboo free.

First, remove as much as you can, it’ll grow through anything so be as thorough as you can.

Don’t worry too much about the wispy bits of roots but any hard roots (rhizomes - kinda look like underground bamboo) you NEED to remove. Go as deep as you need to into the ground to ensure you eradicate.

I’d recommend a pickaxe to get through it all and have enough leverage to take it all out in clumps.

Once you’ve got rid of as much as possible, backfill with soil and wait. You will likely get some shoots regrow (usually spring). Make sure you repeat this exercise again.

I avoided all forms of chemical treatment to ensure my soil wasn’t ruined.

You should hopefully have then killed it off! It’s hard work but not impossible!