"I am a bartender."
Translation:Eu sunt un barman.
They are both correct, but we may prefer one over another in different contexts.
If you just want to point out what you are, you could use either, though I think sunt barman would be a bit more common.
I think we would more likely use sunt un barman to empathize that I am only a barman as if someone would ask you to cleanup the floor and you'd reply with sunt un barman.