Answer: Based on your description, your flower bed sounds very shady. Unfortunately, there are not that many perennials that do well in shade and have red flowers. For instance, you could try a red flowered cultivar of astilbe or possibly a columbine with red flowers. Keep in mind that the perennials will only bloom for only a few weeks, not all season. There are many more white flowered, shade tolerant perennials including astilbe, actaea, dicentra alba, aquilegia, hosta, tiarella, and viola.
If you could work with annuals, you could do an extremely showy display using red and white impatiens.
Ornamental grasses really need sun all day or for at least half the day to stay healthy, so this probably would not be a good location for those.
I wish I could be more encouraging.
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