To make the sushi, combine the rice and 2 cups (480 ml) water in a medium saucepan and bring to a boil. Reduce the heat to low, cover, and cook for 15 minutes. Remove from the heat and let stand, covered, for 10 minutes.
Cut the carrots and bell pepper into thin strips. Cut the avocado into ½-inch (13 mm) slices. Cut the cucumber into 3-inch (7.5 cm) strips.