Bring water and 1/4 teaspoon salt to a boil in a medium saucepan. Stir in bulgur, and remove from heat. Let stand, covered, for 15 minutes. Fluff with a fork, and let stand, uncovered, until cooled, 15 to 30 minutes.
Transfer bulgur to a bowl, and toss with watermelon, parsley, scallions, oil, lemon zest and juice, and 1/4 teaspoon salt. Gently fold in goat cheese.