She said goodbye to me.

Literal

She [topic-は] me [to-に] goodbye [object-を] said.

さよならを言う ('to say goodbye') is the standard verb-object collocation for the act of bidding farewell. さよなら itself comes from 然様ならば ('if that's the way it is...') — a literary conditional that fossilized into a parting word. In modern everyday Japanese it carries a slight weight of finality; for casual everyday partings between friends, またね or じゃあね are far more common. Reserve さよなら for genuine, meaningful goodbyes.