"Farewell" just means "La revedere". The nearest equivalent to "Drum bun" would just be "Safe travels" or something similar.
Agree, each type of official "goodbye" has its translation: Bye! = Pa! Farewell = La revedere Safe travels = Drum bun
"Fare" = (archaic) travel; "well" = competently/in good health. Hence "farewell" = "drum bun".
'Origin: Old English fær, faru ‘travelling, a journey or expedition’, faran ‘to travel’, also ‘get on (well or badly’), of Germanic origin; related to Dutch varen and German fahren ‘to travel’, Old Norse ferja ‘ferry boat’, also to ford. Sense 1 of the noun (money paid for a journey) stems from an earlier meaning ‘a journey for which a price is paid’. Noun sense 2 (a range of food) was originally used with reference to the quality or quantity of food provided, probably from the idea of faring well or badly.'
But, yeah, I wrote "la revedere" too ;-)
Regardless of the Old English, "farewell" is archaic in modern English and no longer used. We just say "goodbye". Surely "drum bun" means "safe journey"? (Native English speaker)
So, regardless of the Old English, what I've wrote in my first comment is actually pretty accurate.
In common Romanian you'll have: See you soon! = La revedere/Pe curând Bye! = Pa! Safe travels/Safe journey = Drum bun
Few exceptions which I don't think you can have a pinpoint translation but you do have an approximate: Good Bye! = Pa pa! / La Redevedere Farewell = Drum Bun ( here i'd rather go with "La revedere" because if I'm not mistaking when you say Farewell you expect to see the other person again - correct me if I'm wrong)
Also when you leave from a group of friends you casually say "Bye" or "Good Bye" in English. In this case mostly used is either "Pa" ( for very close friends or kids ) or "Salut!"
The literal translation of Drum Bun is good road so the inference is you are speaking to somebody who is travelling somewhere (probably by wheeled transport) so; safe trip, have a good journey or bon voyage (which appears international) all work.