Set aside 2 tablespoons of the chopped dulse. Bring water to a boil in a small saucepan. Stir in bulgur and remaining dulse; return to a boil. Remove from heat, and let stand 1 hour. Drain any remaining liquid.
Whisk together oil, vinegar, honey, salt, and reserved 2 tablespoons chopped dulse in a large bowl. Add cooked bulgur mixture, beets, pea shoots, and almonds; toss to coat. Add additional salt to taste. Serve immediately.