Riley, why don't you just click on the links and do some searching of your own?  Haven't we given you enough to get you started?
Rxke,
Looking through some of the links, this has been considered. But, I guess whatever mass you put into the thing as reaction mass must also be accelerated as part of the payload so the net gain may be negligible. Remember the rocket itself will only be about 60 to 100 grams dry and the reaction mass would be about 1 to 1.5kg of water for a 2 liter bottle.
Also, the thing to consider would be pollution, cost and possible health hazards - that's the beauty of using water.
There have been a lot of experiment done with CO2 instead of air and I also read of helium being tried. In some cases, dry ice is used with the water to generate the CO2 pressure.
In one of the links I found, I even saw a guy had designed an electrolysis unit that splits water to charge the bottle air space with hydrogen and oxygen. He then ignites this mixture with a spark unit to give an initial boost. Woooohhhh!!!
http://www2.et.byu.edu/~wheeler/benchtop/hydropyro.htmThe same guy also used a 5 gallon water cooler bottle (normally PC material and not designed for pressure) to loft a pumpkin 20 meters into the air.
Nutters!!!