Ask Mr. Smarty Plants

The first thing we want to say about Bamboo is be careful what you ask for, you might get it. Bamboo does grow fast, many inches a day under ideal conditions, has tough, hard rhizomes (underground stems) that spread the plant. The one we would particularly recommend you NOT try is Phyllostachys aurea (Golden Bamboo), native to China and cultivated for centuries in Japan. Even if we were willing to recommend a non-native to North America or to New York, we don't believe it would do well in the conditions you describe. For one thing, it is a full sun (6 or more hours of sun daily) plant, so your shady conditions might permit it to live but not make the privacy barrier you are looking for.

There is a native look-alike to bamboo, Arundinaria gigantea (giant cane). It also spreads by rhizomes, can grow 3 to 25 ft. tall, requires a medium amount of water, and gets along okay in part shade, which we consider to be 2 to 6 hours of sun a day. It grows in the wild in the American South, but is shown to be native to New York State, although only in the very southern tip of New York. You are correct, it looks as though Smithtown, in Suffolk County, is in USDA Plant Hardiness Zone 6a, in which the average annual minimum temperatures are from -10 to -5 deg. F. There are no hard and fast boundaries between hardiness zones, and microclimates within those boundaries can vary even more. The native Giant Cane is considered hardy to -10, so you should be all right there. Pictures and more information.

Your next consideration is whether you really want that for your natural barrier. We are  going to try to find some other plants native to your area, shrubs or trees, that could serve the same purpose, be more attractive and not quite so invasive. These plants that we recommend will all be native to your area, and because they have been living there for thousands of years, will be accustomed to your climate, soil and rainfall and require less water, fertilizer and maintenance. The problem is finding evergreen trees or shrubs to suit your purposes, but even a deciduous tree would have a limb structure that would contribute to privacy. Follow the plant links to the webpage on each individual plant to get more information.

Shrubs for a privacy barrier 

Ilex glabra (inkberry) - 6 to 12 ft. tall, evergreen, blooms white May to July, high water use, part shade

Morella pensylvanica (northern bayberry) - 3 to 12 ft. tall, semi-evergreen, blooms yellow July to October, medium water use, part shade

Trees

Cercis canadensis (eastern redbud) - 15 to 30 ft.tall, deciduous, blooms pink March to May

Chamaecyparis thyoides (Atlantic white cedar) - evergreen, 40 to 75 ft. tall, low water use, part shade

Ilex opaca (American holly) - evergreen, 25 to 60 ft. tall, blooms white, green March to June, medium water use, part shade

Thuja occidentalis (arborvitae) - evergreen, to 40 ft. tall, medium water use, sun, part shade or shade

Ilex glabra

Morella pensylvanica

Cercis canadensis

Chamaecyparis thyoides

Ilex opaca

Thuja occidentalis