The content of fresh water is usually about 5% air. In your well, there may be a higher content, and/or some other gas such as carbon dioxide coming out of the stone as part of the carbon cycle of rocks. Smells are often from sulphur-containing gases.
When pressure is decreased in the trip from the earth to the atmosphere in your glass, the bubbles become larger and accumulate to rise. Warming the water makes them even larger. In the water-heating trades, we have to know this to get rid of the bubbles because warm gases are much less efficient in heating.
So the process of bringing water to your glass creates the bubbles. While water is in your pressurized tanks and water heater it is still under pressure, so it is more difficult to get rid of that air. An air eliminator tank/vent combination, at the water heater and near the final destination – tap, etc., where the pressure drops to gather the bubbles, can help – if the gases are terribly annoying.
I sort of like a spot of the bubblies – the illusion of a frequent dose of Alka-selzer to ease my headaches – and showering in champagne.