Usually the only time you really need a barrier is along a fence to keep bamboo from getting into the neighbor's yard, and the 4mm plastic stuff will probably work fine. Bamboos are generally pretty easy to control without barriers if you are willing to spend a bit of time to do annual rhizome pruning, and it makes it easier to take divisions too. I only used a barrier around my bissetii because I knew it was perhaps the most aggressive species. Also if you need phyllostachys edulis, you can probably just go to the anderson grove in SC. and dig a few divisions, but it's best to wait until perhaps July or later since the groves are drained of energy from shooting. Here is a link that might be useful: my garden blog

Since bamboo is hollow, I think you might actually amplify the sound. You might be able to block some sound with something taller and wider, but I don't think you would with only 3-4 ft.--the sound will come around and over. If I was going to try something, it would be larger and the side toward the air conditioner would be something softer than wood...perhaps foam, styrofoam, or acoustical tiles (like on a ceiling). Another possibility is heavy cotton batting (something like that is what our dishwasher is wrapped in, and it is nearly totally silent), but that might be more difficult to use, unless you staple it to plywood or a wooden frame. I realize none of those are pretty, but they could be disguised. To avoid digging, make it something like folding screens or 2 double posts on a stand that whatever material you use could be dropped into. I know that is not a good description, but maybe I can draw a picture of it and attach it. Look on Craigslist for free or cheap materials to experiment with--insulating styrofoam is frequently on there, along with misc. lumber and bricks (at least in our area those items are on there almost every day). I wouldn't put a lot of money into it (unless you have another use for the materials) until I had experimented and thought it would work.

That's a very small planter for a large bamboo. Eventually Nigra will look pretty bad in it if you can't divide it often. If you don't mind dividing it often you should be fine. Otherwise bamboo grows great for a couple years or 3 and then looks horrible from being way to overgrown and cramped in a container. Eventually it's just roots and no dirt and dries out very very fast and get's fried or frozen in summer and winter.

You should be able to rent a Ditch Witch walk-behind trencher, but you would need to get one that goes at least 24" deep...maybe deeper depending on what species of bamboo you're trying to contain,