Fill a shallow bowl with water. Working with 2 rice papers at a time, dip the papers in the water, shake off any excess, transfer to a work surface and let stand until softened, 30 seconds. Place a small handful of the vermicelli on the lower third of each rice paper. Top with two strips each of the red and yellow bell peppers, one strip each of avocado and cucumber and a big pinch of alfalfa sprouts. Garnish with a few strips of basil. Press to flatten the ingredients, then roll them up in the rice papers, folding in the sides as you go. Press to seal. Repeat with the remaining rice papers and fillings. When all the rolls are made, cut them in half on the diagonal and serve with the dipping sauce.