Hot gas rises and Air is takes up space

We tried taking a long necked bottle and putting both tap and clay around the neck surround and a funnel.  The idea is that , since the bottle is filled with air and if no air can escape a bottle, then sealing the area around a funnel that is placed inside the top of it, water poured into the funnel should get stuck. But, we could not get this to work. I tried a normal funnel and a funnel shape that I have for squeezing frosting onto a cake.  Even this funnel shape with a tiny opening still let water flow in. So, the next day, we put a balloon on this narrow mouth bottle and then observed. The balloon just flopped over to the side. But, then, in a pan of near boiling water, the balloon filled up with hot air.  So, this showed, since the balloon definitely made a seal around the top of the bottle, that air must be contained in the bottle as there was very little air in the balloon.   I will add pictures later as we forgot to take one in the boiling water.