She didn't die. The blast broke her body and brought her to the brink of death but she didn't die. They were able to get her to a regeneration tank before that happened. The moment she opened her eyes was the happiest moment of Vegeta's life. The moment she saw Vegeta waiting for her on the other side of the glass for her was the happiest moment of her life. At that moment they each realised that all they will ever need to be happy and content is each other.
Having proven his loyalty when it was really called for Goku was allowed to leave with his son. He left shortly after Bulma's recovery, taking a brooding Gohan who refused to except his grandfather's death. Gohan cried for endless nights telling his father all the things they did together. He talked so earnestly about his Grandfather that it made Goku wish that he himself had got a chance to know his father. But that was not to be.
When they arrived on earth, however, a surprise was waiting for them. All his dead friends alive and well stood around to great him. It seems that the Saiyain's had made the mistake of letting Piccolo bleed to death. That of course did not happen. Piccolo recovered in due time and the Dragonballs did not turn to stone. Mr. Popo gathered it and wished everybody back. Gohan was ecstatic to hear this. He wanted to wish Bardock back and he did not want to take no for an answer. But no was what he had to settle for. Whatever Bulma's influence maybe in the future the Saiyains were still the Saiyains now. They could not find out about the Dragonballs, they could not wish Bardock back. In time Gohan did see reason. But he did not like it. Not even Goku really did. But what had to be done, had to be done and of all people Bardock would have understood this.
It was rather ironic that the moment the Saiyains had a future, the moment Bardock's visions of doom and gloom began to fade is when Bulma and Vegeta came together. It appears that the Planet Vegeta was saved because of one blue haired human woman.