If you pull up the green shoots they break off.
If you dig out the roots, and accidentally drop more than an inch of the stuff back into the ground it takes root again.
So there is little alternative but to use chemicals unless you really want to avoid having chemicals in your garden in which case you need to dig down to get it all out and sort through the earth pile too. So we did.
After fifteen inches I experienced the bone-shuddering impact of my fork against something concrete. Excavating away I discovered a paving slab. Widening the search I found the paving slab was laid perfectly next to another and eventually I exposed a flat, paved area underneath the bed which may once have been the base for a shed, or simply a small slabbed area for a table and chairs.
The bindweed grew up through a couple of cracks in this, extending into the compost heap (see previous posts) which I had to move, sorry about the smell.
So, do we use dynamite?
All respect to bindweed. It survives. If bindweed man existed he'd take all the other super-heroes single handed.