Place noodles in a small bowl; cover with boiling water. Let stand 1 minute, and drain.
Place cucumber and carrot in separate small bowls; add 1 tablespoon rice wine vinegar to each bowl, and let stand while cutting and measuring remaining ingredients.
Combine cucumber, carrot, bell pepper, and bean sprouts. Divide into 6 piles.
Place 1 inch hot water in a large shallow dish. Add 1 sheet rice paper to dish; let stand 30 seconds or until soft. Remove rice paper from dish, and place 2 basil leaves in center of paper. Top with about 2 tablespoons cooked rice noodles and 4 shrimp halves. Sprinkle with 2 teaspoons cilantro and 2 teaspoons mint. Pack 1 pile of bell pepper mixture tightly, and place on top of herbs. Place about 1 tablespoon shredded lettuce next to bell pepper mixture.
Fold sides of rice paper over filling; roll up tightly, jelly-roll fashion. Gently press seam to seal. Place spring roll, seam side down, on a serving platter (cover to keep from drying). Repeat procedure 5 times. Serve with Asian Dipping Sauce.