I don't think a fence would do much to block the sound, especially not if it is only on one side of air conditioner. Maybe another way to go is to try and drown out the sound with other things. A small patio fountain and wind chimes perhaps?? Or bring a radio out with you ;-)
CMK

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.

Even using a paint program, I can't draw a straight line to save my life. So I'll try explaining my idea. This would be a rough version, but I'm trying to use materials that are easy to come by, fairly inexpensive, and easy to visualize. If I was going to actually build it, it would be different materials, but this will give you a picture of what I have in mind.
Take 2 cement blocks (the kind with 2 holes in them) and 4 4x4 posts. Place the 2 cement blocks perpendicular to the AC, about 6 to 8 feet apart (no more than the width of your planned wall). Drop a post into each hole in the blocks (will 4x4s fit? I don't know...remember this is just to give you a visualization). Let's say you're using 2x8 or 4x8 foam insulation as the wall material (it comes in different thicknesses)...just drop it between the posts.
When looking for a picture of the foam I'm talking about, I ran across something I didn't know Home Depot carried...sound deadening board. It's cheaper than the foam, in case you have to buy new. I don't know if it would stand up to outdoor use, though. The foam will, although it will have to be disguised for beauty (perhaps with that reed fencing that building stores carry). Have fun experimenting!

Here is a link that might be useful: sound deadening board

Thanks everyone for all suggestions! I got a kick out of "I can't draw" Ha! Believe me, I can relate!!

I don't think the windchime idea would work since there would have to be a constant wind strong enough to make them chime - and it doubt it would drown out the a/c noise anyway. The concrete block with posts is a good idea but not so sure about attractiveness unless I disguise it with something else. My concern about attractiveness is mainly because my beloved HOA may not like the idea of anything being there at all but I figured if I did something that kind of blends in with the landscaping, they may not say anything. Unfortunately, taller and wider is simply out of the question - I'm sure the HOA would go postal over that! The other night, I took a 4'x4' piece of MDF and just leaned it up against the a/c and it worked wonders! It doesn't block it out completely of course, but muffled the sound considerably -- and I didn't give me a start everytime the a/c kicked in. I'll check into home depot's sound board and see if it will hold up outside and see if I can figure out a way to disguise it.

Again, I appreciate all your input!

Unfortunately, skye, there is nothing vegetative that is an effective sound barrier. No trees, no shrubs, no bamboo. Whatever you use has to be solid. A fence isn't going to be effective; a wall, on the other hand, has possibilities. You can put plants on it or over it, but they will be decorative camouflage only.

Kay