How about spirea bush? They get up to no more than 4' in height, can be dense enough to screen, and even get some flowers. They like full sun, too. They're hardy for zones 4-8 or so, and are pretty much maintenance-free. I'd opt for summer blooming varieties in the sun. Golden Princess is a pretty chartreuse with mid-summer pinky-purple blooms that gets to just about the height you're looking for, or at least mine are maybe about 3.5'. I've got a pair by my patio that look really nice.

Here is a link that might be useful: Descriptions of some varieties of Spirea

Trumpet vine would work nicely too. It climbs quickly, brings in humming birds, has lovely orange/red flowers or yellow depending on the color you choose to plant.

Thx everyone for your help. Will look into your suggestions.

Stay away from the trumpet vine very very very invasive and the roots go down to China.

Unless you use trees, you will not have to worry about roots from shrubs or flowers.

I agree with gotta. The first shrub to come to mind was spirea. Maybe holly, rhodys, golden vicary, barberry would work too.