Why do bubbles of gas form on the sides of the bath or glass while or after you have run the water?

It's to do with nucleation sites. If you look at where bubbles form in a glass of beer, they always form on the edges or the surface of the glass and it's exactly the same way that a raindrop forms and it's exactly the same way as a bubble of air forms. You need to have something for it to form on. Bubbles usually start on little peaks and troughs on the surface of the glass. Avid listeners of the Naked Scientists will have a few weeks ago heard Professor Herbert Huppert doing an experiment where he put some sugar into a bottle of lemonade and lots of nucleation sites were formed and the bottle of lemonade exploded. In other words, a nucleation site is a rough area on a surface. If you look at water, the reason fish can breathe underwater is because the water is full of dissolved oxygen and other gases. If you have a rough patch on the side of something such as glass, that can act as a point where the gas molecules come together to form a bigger an bigger bubble. You can see this if you pour yourself a glass of tap water and leave it by the bed overnight. When you wake up in the morning, it will be all bubbly. Those bubbles will form wherever there is a rough patch on the side of the glass.