It speeds up the brewing process because just as you said it adds O2 to the mix. Water with oxygen is aerobic and water with out is anaerobic. Anaerobic water is not good it has all kinds of nasty shit in it. Aerobic water is the perfect breeding ground for the beneficial micros in your tea then you add worm castings, humas, molasses, ands whatever else to feed the micros.
The reason ou bubble tap water instead of using an RO is as mention earlier it takes out the minerals.. The objective is to remove the chlorine, fluoride, ... From the water. I have never tried but putting tap water in a tea brew I'm pretty sure the chlorine will kill the micros. I you let the water sit in the sun for a day to let the chlorine dissipate from the water leaving the calcium and other minerals a bubbler just speeds this process up. There is also a school of thought that adding O2 to water before water the plant will result in more O2 intake through the roots. That's why airoponics systems wook so well for rooting clones.