I don't think there's a place on earth that bamboo won't survive! It depends on what kind of look you'd like. If you're needing something very quick, there's some really good bamboo choices out there. It grows fast and spreads. If you ever think you'll need to remove it, you'll have a problem!

Loquat trees grow fast and dense and have good fruit. Talo trees grow quick, but spread a little.

Wisteria is a pretty choice and there's a thread here about some roses that grow like crazy.

http://forums.gardenweb.com/discussions/3064036/lady-banks-rose-do-you-love-it-or-heave-it?n=11

If you go down High Rd in Flower Mound towards Lake Grapevine there is tons of bamboo growing. It seems to be thriving and doing well! I like the look of it.

I'm sorry to say...red tip photinias.

They grow fast, they get huge, & the foliage is dense & evergreen.

or maybe honeysuckle; if/when it gets out-of-bounds, you can mow it down.

I my own self love coral honeysuckle, which has much better manners, but it doesn't grow as fast.

which you can overcome by planting more of them to start with.

edited to add:

just realized you said neighbors have a 2-story house...

Although Italian Cypress trees are short-lived (15-20 years in Dallas is what I've heard), they're very tall & very slim & they're evergreen.

Best luck!

I would think The Green Tower boxwoods would work, as would Italian cypress trees planted closely together.

Molly

I believe it's the 'Taylor' eastern red cedar (Juniperus virginiana) fastigate doing well in our Dallas neighborhood. They're evergreen and reasonably fast growing, so might be a good solution as long as no one in your family has bad cedar allergies. Believe this would require less annual pruning effort in a 4 ft space than photinia and much less pre-planting work than bamboo, though probably slower growing than either.

Bamboo can be a good privacy option in north Texas if planted correctly and maintained annually. Controlling running bamboo is not that difficult if (and only if) you minimize any escapees with effective barriers and have access to any that do happen to get out along with the time and discipline to deal promptly with their new shoots each spring. After living next to our neighbor's for 20+ years, I've found Howard Garrett's (Dallas area landscaper and "Dirt Doctor" organic gardening personality) advice works pretty well:

Spreading can be stopped by kicking over the shoots just as they emerge in the spring. To control bamboo, cut down or knock over the fast growing shoots in the spring.Then use a sharpshooter or axe to sever the shallowly growing rhizomes. It is not necessary dig the rhizomes out. The plant will die out in the areas treated.

A very good bamboo grade rhizome barrier should be installed around the area you want it to stay in - especially along the property line or adjacent to shrubs or other beds where new shoots could grow undetected or inaccessible. Trouble occurs when it escapes, gets established, and spreads for a few years before someone becomes concerned enough to take action (or a neighbor gets tired of messing with it each spring). Took my brother over three days to clear their new back yard of bamboo that had escaped from their neighbor's. Now just the regular lawn mowing keeps it at bay.

I planted bottlebrush as a hedge shrub and it has grown tall and dense. Our backyard has an iron fence on either side and I feel we have plenty of privacy. Also blocking a view with a pergola is a thought!