@little Froggie I did not know that the torah is called the bible. Thank you so much for clarifying it for me.
Ok it seems that I was wrong about my sources but based on the community I was raised in, It is common for people to say good shabbos to people of the opposite gender. That is what is considered polite. Maybe in your communities this is not the norm. However I am going to trust the Rabbis and the community I am from.