Personally I would avoid bamboo, but there are ways to manage. Firstly, though, don't assume the brick wall you mentioned will be impenetrable @edstrong (I know from experience !).
One can get membranes capable of withstand the mighty drilling power of a bamboo rhizome and, of course, they can be grown in large robust containers (above or below ground), Another way is to plant in an elevated bed/earth mound: because bamboos are shallow "rooting" it is possible to cut off the rhizomes as they emerge from the sides of the planting mound. However ...
I would go with hazel rods, if you have access to, and then, as alternative, willow: willow will provide the easiest self-grow option. A few willow stools cut back each year will provided plenty of rods once stools are established. The rods will need to be thoroughly dried before use of course (else you will have new willows growing in your veg patch) and their dried buried ends might not last much more than one growing year (much like bamboo) in wet soil, but you will have a recurring supply.
Plenty of willows varieties produce long stout rods in one growing season: fast growing, stocky "bio-mass" varieties might be best for your needs, but the old faithful Salix Viminalis would probably do if planted in decent moist soil and annually cut back.