It will never reach the height of a two story home, but I'm assuming you need it only 12 to 15 feet tall, including the tub? Or maybe the tub will be 'on' your patio? It may not reach 15 feet tall in the tub...the growing area is too small.

If you live in an area that would give the plants some Winter protection, there are some Bambusas that will give good Summer privacy, but may lose leaves and thin out some during colder months. They are clumpers and will not spread much at all.

Another idea, would be to plant several pots of a Bambusa and set them on and along the edge of your patio. In Winter, you could move them to a more protected area on colder nights.

To answer your earlier question, here, it would take about 3 to 4 years to get rootbound in the tub at which time it would finally be thick enough for a privacy screen and be tall enough.

Kt