All 3 Uses of

adieu
in
The Aeneid

Make haste to save the poor remaining crew, And give this useless corpse a long adieu.†
Book 2 *

adieu = goodbye

With tears I took my last adieu, and said: 'Your fortune, happy pair, already made, Leaves you no farther wish.†
Book 3

No look, no last adieu before he went, In an ill-boding hour to slaughter sent!†
Book 9

Definition:

a farewell remark (an alternative to goodbye)

Adieu is typically more formal than bye. It comes from the French, à Dieu which literally means "to God" — as in I entrust you to God's care.