All of the fennel bulb is edible. In some older bulbs the stalks or the outer layer can be a bit too tough and stringy to be pleasant, so you may like to remove this depending on the bulb you have. The bulb also has a conical core which can get tough. If you want to remove this, cut the bulb into quarters and then slice out the core. The green, feathery tops can be used raw as a refreshing garnish.