Does it have to be in a container or can it be in the ground? How big an area do you need to cover?

Bamboo starts looking scrappy & tiresome after a while. How about one of those neat looking 'living privacy screens'? You can get ivy, beech, privet, etc. Here's a link.

http://www.impactplants.co.uk/product-category/living-screens/

I'd put up a rigid trellis on top of that part of the fence, you can get brackets to fix it. You could then grow something up it in a pot.

More info required, please, so that we can suggest plants which will be happy:

What is the aspect (north, south, east or west)?

Is the site sheltered or windy?

Can the plant go in the ground, or must it be in a container?

If in a container, how large a container will the site support?

It would need to be in a container. Or two large side by side. I could only think of bamboo as we would need the height.
Thanks all !

With bamboo as with anything else, shrubs in containers will be healthy at a height of no more than 3 times the average of the height and width of the container. For example, a bush in a container 50 cm wide and 70 cm tall will grow happily up to 180 cm tall, but may start to get thin and yellowish if allowed to grow taller. Very narrow species, such as fastigiate yews, or 'Wil Fleming' Yaupon, may get a bit taller with safety. To keep containerized shrubs happy long term, feed them regularly, and tip them out every 3-4 years, prune the roots judiciously, while pruning the top fairly severely, and replace the old compost.