Is money earned from transporting a person wanted by authorities for a bounced check, knowing about it midway through the journey, permissible or forbidden?

It is not permissible to assist an evader of justice or a transgressor in any form of aid, for it is stated in the Hadith: "Allah curses whoever shelters a muhdith (innovator/criminal)." And "whoever shelters a muhdith" is one who supports a criminal, provides him shelter, grants him refuge from his adversary, and prevents him from being justly punished.

As for your situation, there is no blame on you or on your wealth, because you were unaware of his situation and his evasion when he rode with you, and you delivered him to the claimant so that he could reconcile with him.