A better cup of tea is easily within reach no matter where you start.
Good water, good tea leaves and the right temperature and steeping time will always result in an excellent cup of tea.
But no matter tea what you have in your cupboard right now, just changing the water temperature and time can help you get the most of it. Tea is an adventure and we all have personal tastes. Don't be afraid to experiment.
Remember that the sweeter flavors of tea emerge at lower temperatures (170-190F) and the tannins and more astringent flavors emerge in the 180-210 range.
Longer steeps release more tannins, which will overshadow the sweeter aromatic flavors. So removing your tea leaves at the right time is also important.
So if you think your current black tea is too bitter, try lowering the temperature by 10-20 degrees. Pouring your water into a separate cup or pot for 30 seconds before pouring into the one with your tea will get you in that range. So will waiting 3-5 minutes for your kettle to cool.