EDIT (to answer the question up front): The tea without the added caffeine does have bitter flavor to it, but you don't notice it because "noticing bitter" means there's "too much bitter" in the flavor profile. The tea tastes good because the bitterness in it is balanced by other flavors—and that balanced bitterness is part of what makes it taste good.
(As for the second question, you can't. Caffeine has a flavor, and it will add that flavor to whatever you add the caffeine.)
I thought it would be useful to add something here that nopony has mentioned: bitter flavors can taste good in conjunction with other flavors. That bitterness is an important component in the flavor profile of most teas. Tea tastes good in part because of how bitter it is. Adding lots of extra caffeine will make it taste too bitter because caffeine has a bitter taste, but a tea without all of the bitter components wouldn't taste that good either.
For another example, I can taste the difference between Mountain Dew and Caffeine Free Mountain Dew. I prefer the caffeinated version (slightly), because the bitterness of the caffeine balances the sugar better. The caffeine free version is a touch too syrupy, leaning very slightly towards root beer. But there's a ton of caffeine in Mountain Dew, which is why I can taste it over the sugar at all, and even then it's not strong. Contrariwise, I don't like Mountain Dew Throwback at all (the kind made with sugar instead of HFCS). It's not sweet enough, and too much acid and bitter shine through.
Chocolate is yet another obvious example, not as much from the caffeine as the cacao. I like semi-sweet chocolate because the flavor profile is more well-balanced than with milk chocolate (the sweetness doesn't totally mask the bitter flavor), and tasters almost universally prefer cookies made with semi-sweet chocolate when the cookies are already loaded with sugar. Supertasters seem to like chocolate that's much more bitter than an typical taster can stomach, but I don't know why.