RIFT - Bard damage influenced by....?

it depends on what you have set as second soul (likely ranger). If so, it's dexterity and attack power. The bard is a support class, with significant buffage ability and limited healing. you do want to be able to solo, and for that, you will need to choose a second soul that can do adequate damage. Ranger is good because it also gives you a pet to aid you in questing.