Ask Mr. Smarty Plants

It's a little difficult, without seeing a spot, to make definite recommendations for plants. We can, however, make recommendations against sugarcane and bamboo. Both are members of the Poaceae (grass) family, and bamboos, in particular, can be very invasive, and non-native to North America.

Saccharum offinarum (sugrcane) originated in the South Pacific Islands. Other sources say it originated in India, but it is definitely not native to North America. The Lady Bird Johnson Wildflower Center, home of Mr. Smarty Plants, is dedicated to the growth, propagation and protection of plants native not only to North America but also to the areas where they grow naturally. From this USDA Plant Profile Map you will see that it grows only in Texas (probably on the southern coast) and the southeastern states.

It sounds to us like you need something more like a curtain or screen, rather than something the width of  plant ordinarily used to cut off views. You are correct in assuming that one plant of bamboo or one plant of sugarcane would be nice and narrow, especially if you could grow them with only an inch or two between the trunks. Unfortunately, that is not how grasses work. In fact, bamboo is one of the fastest-growing plants in the world. In no time, you would have either plant growing up through your sitting area, over on the neighbor's side and possibly overshadowing and overtaking other desirable plants you have placed in your sitting area.  They spread, like other grasses, by both stolons (above-ground runners) and rhizomes (below-ground). We have no personal experience with sugarcane, but have heard about and seen many gardens in which bamboo has simply taken over and nothing seems to be able to even slow it down.

Usually, what we recommend for a privacy screen is evergreen shrubs that can be trimmed to keep them from getting too high.

If you have space for a lightweight fence, you could try some climbing, flowering vines native to Kansas. These would still require some depth, but not as much as a shrub or an invasive plant. Two we found in our Native Plant Database are Campsis radicans  (Trumpet creeper) (which is semi-evergreen and, alas, also somewhat invasive) and Lonicera sempervirens (Coral honeysuckle), evergreen and capable of being intrusive if not aggressivly cut back. We looked in vain for a tall, narrow shrub native to Kansas and found nothing, again, not knowing the width of the space.

Beyond that, have you considered building or having built a screen, with perhaps wooden woven slats? This might even be designed to provide some shade for your sitting area. In the final analysis, that would probably be no more expensive than buying, planting, caring for and watering plants.