Cut outer stalks and feathery greens from fennel bulb; chop feathery greens to make 2 tablespoons and set aside. Cut bulb into quarters; cut core from each quarter and discard. Thinly slice bulb quarters crosswise into shreds. Reserve outer stalks and any remaining greens for a future use or discard.
In medium bowl, combine shredded fennel, reserved fennel greens, apple, carrot and cherries.
Pour salad dressing over salad; toss gently to coat. Serve immediately, or cover and refrigerate until serving time.