I have never grown bamboo but MO Botanical Garden says blue fountain clumping bamboo is hardy here and would grow in shade. I thought of leatherleaf viburnum but I have never grown it myself. I have seen it as a foundation plant and thought the leaves were interesting. It gets both positives and negatives on-line so you would need to research it. I think it would be evergreen in Northwest Ark and is more tolerant of shade than some other viburnums. If I had neighbors overlooking my yard and with a good view in my window, I think I would look into some sort of cedar lattice structure made of 4 by 4's for a frame with wood lattice on it. Then you could grow a vine or something in front of it. Plants can grow fast but usually it takes are few years unless you buy big plants to begin with. I am not handy so I have no idea how to build something. Also you may need something really long. Good luck.

I don't have any experience with bamboo but I believe there are some types that are very aggressive spreaders and some that are not. There used to be a nursery in Arkansas that specializes in bamboo. I wonder if it's still there.

If you decide to go with vines, the native coral honeysuckle (lonicera sempervirens) would attract a few hummingbirds and butterflies for you to watch from your sunroom. There are several named cultivars of that same species. 'Major Wheeler' is supposed to be one of the best bloomers so I will leave a link for that one below. It wouldn't have the same wonderful fragrance of Japanese Honeysuckle but it won't be nearly as invasive either. It has a VERY long bloom time.

I'm fairly certain lonicera sempervirens would create a screen must faster than most shrubs, stay the size you want, and do well with a few hours of afternoon sun like you mentioned.

Vines tend to extend a ways above their support and then just grow back down on themselves. For instance, if you wanted your screen to be about eight feet tall, you might want five foot supports; taller supports for a taller screen. That was a really rough guesstimate so you'll want to get some more opinions. Gardenweb has a Vines Forum or you might try asking in the Perennials forum since it has a lot of visitors.

Here is a link that might be useful: 'Major Wheeler'