You don’t mention your growth conditions or whether there is a fence on not, so let me introduce you to our Native Plant Database that can help with finding plants for particular situations. One way of using the Database is to go to the Recommended Species Lists. Click on View Recommended Species Page, and then click on Virginia on the map. This will bring up 122 commercially available native plant species suitable for planned landscapes in Virginia. This is more information than you need, so go to the Narrow Your Search box to the right of the window and make the following selections: select Virginia under State, Shrub under habit, and Perennial under duration. Click on the Narrow Your Search button and the list is reduced to 30. Clicking on the scientific name of each plant will bring up its NPIN page that has plant characteristics, growth requirements and photos. These can help you select plants whose growth requirements fit your growing situation.
You can control the height and width of your screen with careful pruning.
Another approach is to plant an evergreen vine on trellises. This time, use the Combination Search Box on the Native Plant Database page. It works similarly, so make the same selections as before, except select Vine instead of Shrub under habit, and click on the Submit Combination Search button. This brings up a list of 63 native species to choose from.
For help closer to home, you can contact the folks at the Arlington County office of Virginia Cooperative Extension.