What is the fastest growing plant for a privacy screen?

Bamboo is real fast, although it is invasive, so might want it to be contain

Don't do bamboo, you will regret it. Many places are making it illegal to plant bamboo.

You don't say where you are, so I suggest you ask at a good local nursery, or contact your state's Cooperative Extension agency. They will know what is good for your region, and what to stay away from.

What is your location

try a honeysuckle or trumpet vine

nandina

Russian Olives

I agree with posts above, not knowing what zone you are in limits the helpfulness of the answers. The best answer has already been given... check local nurseries, garden centers or your county extension agent. Bear in mind that fast growing plants have their own problems...invasiveness, longevity (many fast growing plants are also short lived) and strength (fast growing plants tend to be subject to more damage from frost, wind, even heavy rains). Carefully research the bamboo variety, if you choose to go that route, making sure that the cultivar you choose will not overcome the space. If it were me, I would try to find a native plant, with something to attract birds or other pollinators, because they can use all the help they can get. Native plants will do well in your space, and wildlife visits are fun to watch. If there is a fence or other support, most vines grow very quickly, and can cover large spaces with minimal expense.