
The translation is overall very well made, but there's one, important misunderstanding regarding the main line.
"Bella" is female, while a word like "ciao", not having any gender, would be automatically associated with the male form, which is the one used to cover anything that doesn't have any assigned gender in Italian (e.g. loanwords are for the vast majority masculine, except some exceptions usually linked to some very specific reason). Hence, "bella" is most definitely not an adjective of "ciao", but a substantive, referring to the partisan's woman, to whom he's talking to throughout the song ("tu mi devi seppellire lassù in montagna, sotto l’ombra di un bel fior"): http://www.treccani.it/vocabolario/bella
The most basic and direct translation of "bella, ciao" is surely "bye, beauty", you may play a bit with the line, but that's it means in any case. "A fine farewell" or "a fine hello" are translations that went very astray from the actual meaning.
A nonlyrical guitar/accordion version:
https://www.youtube.com/watch?v=_Ij5JaEIcPc