Japanese Arrow wood Bamboo(P.japonica) is what I would go with for a few reasons. It can handle 0 degree F. It has large leafs so it will block better. Its a small clum, thus, a bit easier to control. It grows fast. It will get to 15-20 feet.
I think others will chime in and give you a smorgasbord to choose from.
The link will take you to a site that has a few photos of hedges of this bamboo.

Here is a link that might be useful: Photo examples

This post was edited by botanicalbill on Sat, Jul 13, 13 at 13:48

What is the sun exposure and how hot does the area get? That is not a lot of space and am wondering if the plants in the photo are going into the same planting bed. P. japonica is a nice, cold hardy bamboo that I have grown locally, so no problem with hardiness, but it is a runner and if conditions are good, and there is no rhizome barrier and/or you do not rhizome prune on an annual basis, the strip be dominated by the bamboo. Black and Golden Bamboo will get taller faster but they too are runners. There are clumping Fargesia, but if your exposure is too hot and sunny, they will struggle--and they are expensive--initially. I have a 7 foot wall of Fargesia rufa, but it did take 4-5 years to get there (not instant), and it only thrives due to relatively , cool, shaded and humid conditions. Not trying to discourage you from bamboo but depending on the sun condition, there may be other choices (espaliated grapes, figs, Magnolia 'Little Gem' etc.).

Hi guys! Thanks for answering!
The area gets a decent amount of light and It has a western exposure so, so at least 8 hours? So it might be too hot for Fargesia?

To be honest, we have been thinking about running bamboo since it doesn't require as much space it seems? I actually want to expand my sub-irrigation garden so that's the reason why I want to limit the bamboo to just a "trough" 18-inches by 18th ft. We are prepared to install a rhizome barrier. I don't need a super thick hedge that completely covers the whole wall visually. A decent amount of coverage would be good the smallest space possible. In my head something with very straight culms, very densely grown or thicker culms spaced closely together would work too. I like the idea of an almost architectural look as opposed to a thick dense hedge.

I'm also open to other suggestions of how to screen this wall that doesn't take up a lot of space. :-)

Be very careful before you opt for the running bamboo route. One of my concerns is proximity to your house! Maybe others can chime in on that angle. Personally, I think an urban, western exposure in our super torrid summers would overwhelm the Fargesia (which I believe are basically, subtropical highland plants)--they will also take longer to get the verticality you want. What about something like sky pencil holly?

Here is a link that might be useful: Pencil holly

@Botanicalbill:
I like that arrow bamboo - do the culms. From my google search, its a running bamboo so a rhizome barrier is suggested? I really like that one image of the thinned bamboo screen. Thinning is like pruning right? It'll grow right back? Someone was also telling me that if you lop off the top of bamboo, it won't grow any taller, is that true? Our conditions are very hot and humid in the summer (like this heat-wave we've just had) and this western exposure is pretty sunny all day long.

@Njoasis:
The end of this dirt patch is approx 9ft away from the back addition. Do you think that is too close even with an installed rhizome barrier? I'm not keen on the look of the pencil holy. The density of it might seems to be overwelming for this space (yes, I know, its quite enclosed already.) Any other

What about taking a tree and creating an espalier? If you want deciduous, you could use fig trees. If you want evergreen you could use Little Gem Magnolias (which are sort of dwarf for Magnolias), or laurels. Basically, you are taking a tree and training in to grow in one, vertical plane (against a wall).
Little Gems are slower growing but I guess you could use a faster/larger growing cultivar. The one in the picture is 'Victoria'. I planted it 4 years ago, took it home in the back seat of the car--so, we are not talking about growth at a glacial pace necessarily.

That is true, a clum is a stick of bamboo that is like the trunk of a tree. Once they pop out of the ground it will take about a month for them to get to their full height. Once at that height, if you top it, they will get no taller but will probably get bushier. The next year you may have hundreds of new shoots (clums) coming up next to each other. They will grow to their full height, if you top them, they will bush out. You can prune off the branches that grow outward. This way it covers the wall but doesnt stick out. Yes, this type of bamboo is a running type.