What scientific principal is at work in a bag of tea being brewed even in still water?

A lot of different processes are at work. But basically, this is diffusion, and to some degree, solution (dissolving of substances into the water). Even in water that is "perfectly still" as in that there are no noticeable currents or motions, the molecules in the water are constantly moving. The hotter the temperature, the faster the molecules are moving. This is why you brew tea with hot water--if you use cold water it will "brew" much, much slower. The molecules bump into each other and slowly, the substances in the tea start dispersing through the water. Some of the chemicals dissolve and form a solution in the water (these are clear but may effect the color of the cup). Other substances do not dissolve, but instead, form a suspension (whole particles that float through the water). These give tea the cloudy or opaque quality. Even if you don't see motion, the tea is still moving. Because the outside of the cup is cooler than the inside, a heat differential forms, which creates a motion...and you get a convection current. So convection is another process at work. Lots of different things going on at once!