In a bowl, mix cucumber and salt; gently crush slices with your hand until they feel limp. Let mixture stand for 5 to 10 minutes.
Meanwhile, dice bell pepper into 1/8-inch pieces. Sort through bean sprouts and pinch off and discard any discolored tips. Chop the arugula very coarsely.
In a wide serving bowl (3 to 4 qt.), mix vinegar, fish sauce, sugar, and ginger.
Rinse cucumber slices well in cold water, then squeeze slices gently to remove excess moisture. Add cucumbers, bell peppers, bean sprouts, and arugula to bowl with dressing and mix to coat. Spoon onto plates.