Rockets will not work in space. As soon as the fuel was thrust out of the rocket, the vacuum would immediately swallow it up as fast as it came out.
Also, when you put air into your water bottle, does it push past the water and sit on top of it?
You have no proof other than "because that's what I think" to say that rockets won't work in space. The vacuum of space won't "swallow" the fuel. The intense pressure created by the burning fuel will be ejected into space, where it will quickly de-compress. However, the force with which it is ejected will create an equal force in the opposite direction, resulting in thrust for the rocket.
Yes, air is less dense than water, so the air rises to the top of the bottle as the bottle is pressurized. However, since all the contents of the bottle are under the same pressure (water and air) the water remains more dense than the air, and the air stays above the water. When the valve is opened, the air cannot force its way past the water, due to the water's greater density. This means that the water is ejected first, and if any pressure remains after all the water is gone, the remaining pressurized air will also vent from the bottle. Unless the rocket turns upside-down or is severely agitated, the air will remain above the water and the water will come out first. The water will
not force it's way back down through the water and come out first.
If I have a container full of liquid I can pump pressurized air into the top of the container to force the liquid out the bottom. The air will not force it's way past the liquid and come out first.