The armory bonus is bonus exp you automatically get for every battle-job wich is not your highest leveled battle-job. So when you have a level Summoner 70, you will get the armory bonus for GNB until you also hit level 70 with him.

The best way to level are indeed dungeons, but since a lot of people want to level GNB and DNC the queue times will be long, because there are not enough healers. So dungeons are only a real option when you have a healer friend who helps you out, otherwise Heaven on High, PvP and Fates are the way to go.