How do I keep finely chopped green tea from getting bitter?

I bought a sampler pack of 105 teabags from a highly recommended Etsy seller with sky-high ratings. The tea is here, in tea bags and very finely cut. If I steep for a short time, remove the teabag, and drink it as soon as it's cool enough to drink, it's delicious. It's chopped so fine that quite a... show more I bought a sampler pack of 105 teabags from a highly recommended Etsy seller with sky-high ratings. The tea is here, in tea bags and very finely cut.

If I steep for a short time, remove the teabag, and drink it as soon as it's cool enough to drink, it's delicious. It's chopped so fine that quite a bit of the leaf dust settles out of the bag, however. If I steep it for a short brew time, remove the teabag, and then continue to let it steep and cool as I work it gets terribly bitter anyway! There's too much tea dust that continues to brew! Is there a fix for this?
Update: Donna,

Thank you, but I use water from a Keurig, so it's below boiling. I drink a LOT of green and white tea, and have either tossed other brands that are bitter or have not had this problem with them! The seller has so many high ratings I wonder if I'm doing something wrong.
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