Mix the bass, shrimp, cornstarch, ginger, Shaoshing, soy sauce, sesame oil, red chile, salt, white pepper, chives and mushrooms in a medium bowl until well combined.
Working in batches, lay out 8 of the wonton wrappers on a work surface and place a teaspoonful of the seafood filling into the center of each. Rub the outer edges of the wrapper with water using your finger and then place the wonton into your hand. Fold the wrapper into a triangle, pressing the edges together to seal in the filling, and then create 6 to 8 pleats along the sealed edges using your thumb and index fingers, pinching well to adhere. Repeat with the remaining filling and wrappers. Lay the carrot slices in a bamboo steamer and place a dumpling on top of each.
Fill a wok or large skillet with 1 inch water and bring to a simmer over medium-high heat. Place the lid on the bamboo steamer and lower it into the wok. Steam the dumplings until the fish is cooked through and the dumpling wrappers are translucent, 5 to 7 minutes.
For the dipping sauce: Whisk together the cilantro, sesame oil, soy sauce, vinegar and chiles in a small bowl until combined.
Serve the dumplings warm with the dipping sauce on the side.