If the bindweed is well away from other plants, or has wound its way around the bamboo canes, the best way to get rid of it is to use glyphosate weedkiller, like Roundup. Liberally spray the plants, especially where the roots come up from the ground, then allow the weedkiller to soak into the root system.

The best way to get rid of bindweed is to cut it off at soil level. Don't bother pulling it up; it will just sprout wherever you tore the roots--and it is virtually impossible to get all the roots out.