We feel really, really bad about bamboo. It is not only invasive but non-native to North America. At the Lady Bird Johnson Wildflower Center we deal only in plants that are native not only to North America but to the area in which they are being grown. See this eHow website on How to Get Rid of Bamboo to demonstrate why you do NOT want to plant that.
Grasses are what you need. Their extensive fibrous root systems hold the soil in place. Here are a few that should do the job:
Chasmanthium latifolium (Inland sea oats) does well in part shade and shade and on stream banks.
Andropogon glomeratus (bushy bluestem) requires full sun (6 hours or more per day) and moisture.
Tripsacum dactyloides (eastern gamagrass) grows in part shade (2 to 6 hours sun per day) and does well on stream banks.
Andropogon gerardii (big bluestem) grows in sun and part shade and can withstand flooding.
Muhlenbergia lindheimeri (Lindheimer's muhly) requires sun and often found by streams.
Panicum virgatum (switchgrass) for sun and part shade and grows well in damp places.
The following shrubs, along with the grasses, should also do well to help control erosion.
Cephalanthus occidentalis (common buttonbush) grows in part shade and shade.
Forestiera pubescens (stretchberry) grows in sun, part shade and shade.
Sabal minor (dwarf palmetto) grows in sun, part shade and shade.
Lindera benzoin (northern spicebush) grows in sun, part shade and shade.
Malvaviscus arboreus var. drummondii (wax mallow) grows in part shade and shade.
Prunus rivularis (creek plum) grows in part shade and is good for erosion control.
Here are photos from our Image Gallery: