To be "bent on" or "bent upon" something means to be determined to do it, or to insist on doing it. "I told him he should take his car to a repair shop, but he's bent on fixing it himself." In this case, the author is describing the traveller's brain as though it is purposely tormenting him. He feels as though his brain is deliberately refusing to adjust to the new time zone, and he wonders why his brain insists on doing this.

It means “determined to,” in the sense of having a plan or objective to accomplish a particular goal. “His brain seemed determined to torment his body.”