The plural possessive of boss is bosses’. The Hallmark Card holiday is Boss’s Day, because it assumes people like you and me have only one boss. Even if you have more, you will wish each of them a singular Happy Boss’s Day.

On the other hand, if you are keeping a birthday list of multiple bosses, you would say bosses’ birthdays. Notice that birthdays has to be plural too. This is another way to see that Boss’s Day is the singular possessive.