I think I know what you're trying to say. When you said, "You let the excess air out when the water evaporated", it didn't make any sense. There's no air getting in or out. But perhaps you intend for the bag to expand during evaporation.
A black bag in the sun is different. You are literally heating the air inside. This phenomenon will work whether there is moisture present or not. The atmosphere exerts a pressure over the surface area of the bag. The total force is this pressure multiplied by the surface area. To expand the bag will do work against the ambient pressure, which requires energy--in this case from the sun. The interior air is now at the same pressure, but is less dense, causing buoyancy.
In the case of an evaporating drop of water, the bag will also expand, requiring energy to do the work. At first I thought this was impossible...where does the energy come from? Then I realized that the drop will draw energy through the bag membrane from the ambient air that it needs for evaporation. The air just outside the bag near the water droplet will become a little cooler as a result--like the evaporator in a refrigerator. Unfortunately, as has already been mentioned, the minuscule expansion and difference in density would not be enough to provide much lift.
Don Kansas City