Do I need a to add a vapor barrier to my downstairs bathroom ceiling. The ceiling is made of 1X4 cedar boards. There is gaps between the boards. (16th to one 8th inch). The bath room is agaist the back wall of the house. There is a small ceiling fan.

Need more info; do you have a "ceiling" fan or an "exhaust" fan? The vent would be right about ground level near the bathrooms exterior wall. Now for the ceiling. Your boards are probably tongue and groove but there may not really be "gaps" straight through. Try sliding a piece of paper or something between the boards and if the paper goes all the way through then no need to read the rest of this.

Many saunas are made of cedar for just that reason due to their favorable reaction to moist environments. So if the wood is cedar and in good condition then your fine for having that as an exposed material. Take a very hot 15 minute shower. If you have water collecting on the ceiling like rain drops then something is wrong. If you have an exhaust fan turn it on BEFORE showering and there should not be much steam in the room and if there is it should be pretty high up. If you have a large mirror use that as your steam level guide, it collects from the ceiling downward. If you do have a ceiling fan and it is the proper size, connect a nice twist timer to it. Most people turn off the vent when they are done with their shower but should leave it running for another 5 or 10 minutes.

I agree we could use better/more details but the basic answer is no. Vapor barriers are not needed between floors of a home. However you sure do need a barrier on the exterior walls.