In a small bowl, whisk lemon juice, olive oil, mustard, and honey to blend. Add salt and pepper to taste.
Trim stalks from fennel; chop enough feathery green fronds to make 2 tbsp. and reserve. Cut heads in half lengthwise, then shave into paper-thin strips (see Notes) or cut into thin slivers.
In a bowl, combine fennel and bell peppers. Drizzle with dressing and mix gently to coat; cover and chill at least 1 hour and up to 1 day (see Notes). Just before serving, sprinkle with reserved fennel fronds.
Note: Nutritional analysis is per serving.