My interpretation (for what it's worth):

The singer doesn't have a literal key to an automobile. Nor is he literally "billed up and bound to go". (He doesn't have passage booked on a train.) He doesn't have the money for either of those. He either spent all his money on the woman who wrecked his life, or she took it from him.

The only "key" he has is the freedom that comes from admitting he's in a bad situation and needs to do whatever it takes to get out of it. He may hitchhike, jump a freight train, or use his own two feet. Either way, he's gone.