When you say lust for power, you mean her DS apearence? If not I would disagree with you. She had an obsession to prove herself worthy of her gift. Remember that she is already a hero when you first meet her, so she tries to act a perfect jedi not fully understanding what that is. I think her story is dramatic not because of her backstory but because of what she goes through during the game. She chooses to save the PC life, linking her self to the former dark lord of the sith forever. Although she could have just left Revan to die. She sucrifices her self for Revan for the second time, hardly the actions of a powerhungry person. She falls to the darkside (after a week of torture, unlike Juhani). And if you choose to redeem her (which is the proper LS thing to do, considering what she has done for you), she comes out not afraid to be herself anymore and not hiding behind an image she made for herself.
Bastila's story is quiet tragic in a way. What makes her deep is that she goes full circle like Revan realizing on the way things about herself and about people in general. It fits in the whole theme of the game which is redemption. She redeemes you and you get the chance to do the same thing for her. You get to change sides at the beginning Bastila faces Darth Revan and at the end of the story it's the other way around.