I lived in Asia for many years, where I began drinking tea every day.
Use a strainer. You could also use a coffee filter or a cup with a lid. Use the lid to hold back the leaves as you pour the brewed tea into another cup.
Honey works, but usually if a tea is too bitter, the temperature of the water used in brewing was too high. You might also try reducing the amount of tea leaves used.
I would try Adagio or Art of Tea
I've found it difficult, if not impossible, to find good loose leaf teas in all but the biggest US cities. And even then, it's not easy, which is why I generally buy my teas online.
Adding to my previous comment, here's a review and comparison of some popular online tea shops: http://www.letsdrinktea.com/buy-tea-online-shop-review/
I would try Art of Tea or Adagio Teas. Both have large selections of quality teas for affordable prices.
I love gin $ tonics. Vodka and tonics, too. I don't like sweet drinks.
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