Ask Mr. Smarty Plants

I recommend a mixture of grasses, herbaceous plants and small shrubs.  Grasses are very effective at holding soil in place because of their extensive fibrous root systems, but covering your steep bank with one kind of grass only could be a bit boring. Monocultures are generally not the best idea so choosing two or more grasses and interspersing them with some herbaceous plants and small shrubs will give you an interesting and effective means of controlling the erosion.  Since you didn't say, I don't know the moisture and sun availability.  You need to check the "Growing Conditions" section for each species to see if the required environmental conditions are compatible with your site. The cheapest way to carry out your project is by sowing seeds. However, since you would be sowing the seeds on a slope, you will probably find that rain will wash the seeds away before they have had a chance to germinate. You might be able to find grass plugs or nursery plants available for sale. They will be more expensive than the seeds but would have a better chance of setting their roots before rain could wash them away. Another possibility is to use erosion control blankets to stabilize the erosion area. The erosion-control fabric works by slowing the runoff water and allowing sediments to fall out rather than be washed away. Seeds are sown under the erosion-control material and grow up through the matting when they germinate. You can also insert plants into the soil by cutting through the matting. The roots of the plants that are growing through the erosion-control material anchor the soil to stop the erosion. If you use erosion-control blankets made of biodegrable material, they will eventually disappear leaving the plants to control the problem. 

 Grasses:

Elymus canadensis (Canada wildrye or canada wild rye)

Elymus virginicus (Virginia wildrye)

Panicum virgatum (Switchgrass)

Sorghastrum nutans (Indiangrass)

Schizachyrium scoparium (Little bluestem)

Herbaceous plants and small shrubs:

Monarda fistulosa (Wild bergamot)

Phlox divaricata (Wild blue phlox)

Phlox subulata (Moss phlox)

 Artemisia ludoviciana (Louisiana artemisia)

Dasiphora fruticosa ssp. floribunda (Golden-hardhack)