Ask Mr. Smarty Plants

You must not live in an area where minimum distances between a structure and the property line are required, worse luck. Bamboo is not only a bad idea because you are in what is ordinarily a pretty arid climate, but also because it can be extremely invasive, and simply take over. See this invasives.org website on Phyllostachys aurea, Golden bamboo for more reasons why you don't want that. In addition, bamboo is native to China. The Lady Bird Johnson Wildflower Center is dedicated to the use, care and propagation of plants native not only to North America but to the area in which they are being grown. 

It also would be difficult to get any screening shrubs growing without some supplemental water, especially in the first months after planting, and it would take several years for even the faster growing shrubs to get up high enough to give you any real screening. Without knowing what height you need to cut off the view of your neighbors' window, we are going to recommend some really tall native grasses (bamboo, by the way, is also a grass, member of the family Poaceae) and a couple shrubs for starters. Beyond that, about all we can think of is a tall fence, or suggesting curtains to your neighbors.

Follow each link to the page on that plant to learn its expected height and culture needs. Obviously, you need something evergreen, as you already pointed out you couldn't see into the other building until the leaves started dropping. 

Grasses for screening in Central Texas:

Andropogon gerardii (big bluestem) - warm season perennial, 4 to 8 ft tall

Sorghastrum nutans (Indiangrass) - 3 to 8 ft. tall

Shrubs for screening in Central Texas:

Ilex vomitoria (yaupon) 12 to 25 ft. tall, evergreen

Rhus virens (evergreen sumac) - 8 to 12 ft, evergreen

Sophora secundiflora (Texas mountain-laurel) - to 30 ft. tall, evergreen, poisonous seeds

From the Native Plant Image Gallery:

Andropogon gerardii

Sorghastrum nutans

Ilex vomitoria

Rhus virens

Sophora secundiflora