"De vrouw zegt hem goedendag."
Translation:The woman tells him good day.
In English you would not write this, you would say "The woman says good day to him"
Both work technically. Itsjust a matter of punctuation 'The woman tells him "Good day"' vs 'The woman says, "Good day" to him' you would not use 'The woman tells, "Good day" to him' though.
Why not "bids him good day"? Might sound a bit old fashioned , but seems the most appropriate translation here, as in German and Dutch you really 'say someone good day', direct dative, and not TO someone.
English is not my language, but I thought that "Good day" was used for "Good bye" in English.
The term "Good Day" can be used as both a way of greeting someone as well as a way to say good bye. It is rather old fashioned now and you're not likely to hear it from most people under 30 anymore.