Make toasts: Put oven rack in middle position and preheat oven to 425°F.
Arrange bread slices in 1 layer on a large baking sheet and brush top of each with 1 teaspoon oil. Bake until golden, about 12 minutes.
Make chickpea purée: Slip off skins from chickpeas with your fingers (discard skins). Blend chickpeas, water, oil, lemon juice, and salt in a food processor until very smooth (mixture will appear whipped).
Assemble bruschette: Spread toasts with chickpea purée and serve topped with arugula salad.