Bitter tea is usually a sign of oversteeping. If you're using teabags and leaving the teabag in your cup (resting toward the bottom), that's why.
Here's how to make a proper cup of black tea:
Boil fresh, cool water. Place into an infuser one teaspoon of black tea leaves per six-to-eight ounces of water used. When the water boils, pour a small amount into your teapot and/or mug (depending on how you're brewing), swish around, and discard. Place the infuser in your teapot or mug; pour the desired amount of water. Allow to steep no longer than five minutes. (Use less time if you want a weaker brew.) Remove tea leaves; do not compress.
Hope this helps!