Where do the bubbles in a glass of water come from?
Gases are less soluble in warm water than cold water.

The bubbles are likely from dissolved gas coming out of solution as the water warmed.  

The bubbles are unrelated to self-ionization of water.  The self-ionization does vary somewhat with pressure, so at an extreme depth in the ocean you might need to consider what Kw is, but not in a glass of water.

The solubility of gases increases with pressure, so on this basis it is more likely that you would have bubble appear near the top.  However, the pressure is only 1-2% greater at the bottom of the glass compare to the top.  There may be fewer nucleation sites (such as tiny scratches) near the bottom of that particular glass.  Also, if the bubbles move up along the wall sometimes, it would be logical that there are less at the bottom.