I believe that the layperson can say "God bless you" to everyone, other than a priest/bishop, through whom God bestows blessings on His faithful.
Therefore, it would be inappropriate to tell a priest "God bless you".
My mom always gives me her blessing. Every single day of my life.
She would stop us at the door before we would go out to school. Make sure our coats were buttoned, that we had our lunches, and would finally word a prayer over us and make the sign of the cross over each of us...and then push us out the door to run to the bus. As an adult, she would get up each morning and see me off to work the exact same way.....and now that she is bedridden, I go to her before I leave the house, and she does the same thing from her bed.
I am soooo very blessed.
What do people usually say to each other in parting? Well, "Go with God", "may God watch over you", or "see you next week!" come to mind.