The only options that work with bombers (besides Heal and Do Nothing) are rebase to another city (hit the rebase icon and then click on the destination city, which does have to be in range and cannot already be at capacity (6 air units, or 10 with an airport)) or attack an eligible target (enemy (i.e., at war) unit or city that is in range -- note the range is less than the rebase range, because an attacking plane has to make it back to their original city).
When attacking a target, you will be shown in red the maximum range of your bomber and eligible targets will be highlighted -- works very similar to city bombardment.
You must be at war with the civ that owns your bomber target before you can attack.