Vines - If all you have is a very-narrow area, then consider vines. They will climb a fence or trellis for privacy in a compact space. A few options are Star Jasmine Vine and Florida Flame Vine are fast growing, full-covering options.
Bamboo - I know what you are thinking, I don't want bamboo going everywhere in my yard, but you're thinking of running bamboo. All of the varieties that we carry are clumping bamboo, and while over time the clumps can get large , especially on big varieties like Giant Timber, many maintain a smaller profile. For bamboo tips, see the garden article below.