I watched a video interview with the 10th heir of Twinings Tea Company, that has been merchandising tea for over 300 years. In the interview, among talking about the family history, and the story behind their bestselling tea flavor—Earl Grey—he talked about the best way to brew tea, whether using loose leaves, or a tea bag.
To extract the most flavor out of tea, he recommended bringing cold water to a boil, and removing the kettle off the stove once the water starts boiling. His theory is that the flavor is extracted through the air in the water, and continuing to boil the water further, will reduce the amount of air in it.
For green teas, he recommends letting the kettle set for 5 mins, then pouring the hot water over the tea, and for black teas, he recommends pouring the hot water immediately over the tea. The heir advised against removing the bag, or repeatedly dunking it in the water during brewing, because that only changes the color of the water, and makes the tea bitter without extracting flavor. On the contrary, he recommends leaving the tea bag still for 3 minutes, and then throwing it away, enjoying the flavorful tea, adding milk, or lemon, but never sugar, as it masks the tea flavor.
I followed his advice verbatim, and while I am not sure if the effect is psychological or real, I drank the best cup of tea in years. No bitterness, no sweetness, just great tea flavor.