General:
* Poet
* Minstrel
* Singer
* Storyteller
* Verse-maker
* Lyricist
More specific:
* Troubadour (for medieval French poets)
* Skald (for ancient Scandinavian poets)
* Rhapsodist (for a wandering poet or performer)
* Laureate (for a poet officially recognized for their work)
The best synonym for "bard" will depend on the specific context in which you are using it.