please, raboissai- i never heard of a girl going over to a 50 yr old man, flutter her eyelashes and say “good shabbos”. Somehow, in my imagination, the wrong relationships start out very differently.
As to whether or not saying g’shabbos is correct- i’d say it’s a chumra/geder (an admirable one). We can’t touch a strange man/woman, we try not to speak to a strange man/woman