Bamboo typically are not drought tolerant: they like lots of water. Unless you are prepared to water it or provide dripper irrigation, you are not going to be successful. Do you see any of your neighbors who are successfully growing bamboo? If so, I suggest you ask them what species it is and how they maintain it. Or you could ask a local nursery.

I wish I could be more helpful, but what you describe is not an ideal situation, and I don't think it would help you by suggesting any plant names unless you want to alter the watering situation on you property.

Maybe Thamnocalamus Tesselatus. Supposedly can take heat, but I'm sure it will still take a certain amount of water, especially the first year.

Mexican Weeping Bamboo.(Otatea acuminata ssp. Aztecorum).

Alphonse Karr