Bigger Thomas feels alive and free from the oppression of white society when he thinks about or commits crime. However, it is that same white society oppression that scares Bigger and keeps him from expressing himself in more constructive, positive ways.
For example, when Gus, Jack, and Bigger contemplate robbing Blum's store, Bigger is both enthralled and scared to death with the idea. Although Bigger has participated in many other crimes,they were all committed against other blacks; Blum is white. And although Bigger never does in fact rob Blum, the thought inspires Bigger to act out in demonstrative ways. The unintended murder of Mary Dalton is very, very similar. Bigger doesn't want to commit the crime, but he cannot resist the feelings power and control the acts bring him.
As Mr. Max argues in the his closing statement near the end of the novel, Bigger Thomas rebels against the law and status quo of the larger white society that has oppressed him all of his life. Bigger Thomas's criminal acts are his attempts--albeit very misguided attempts--to exercise his free will against that society and take control of his own life. Like an individual being suffocated (again, the connections here to Mary Dalton's death are apparent), Bigger Thomas's crimes are his attempt to breathe and end his suffocation at the hand's of white society.