Tea infused with caffeine
The average caffeine content of black tea is around 50mg/8oz.  Green tea is much lower in caffiene, around 30mg.  My guess is that you're trying to replace the caffeine kick of coffee, which is more in the 150mg/8oz range you specify.

Further, you can increase the caffeine content of black tea simply by brewing it longer.  Assam tea is particularly high in caffeine.

So my first suggestion is that you just drink three mugs of very strong brewed black tea, rather than adding powdered caffeine.

If that doesn't satisfy you, the time-tested way to reduce bitterness in tea -- as any Englishperson could tell you -- is to add milk or cream.  I see no reason why that wouldn't help cover for the bitterness of powdered caffeine just as well.