I would presume they wouold take the tilt train from Brisbane. There is an airport train from the airport to the city, then you go to a different platform in the same area to catch the tilt train. I did the same 3 or 4 years ago. Flew up from Melb to Brisbane. Walked out of the airport and straight onto the train to the city, got off that in the city and walked a little way to the tilt train and took that to Bundaberg. I know it goes further north but can't help with details of towns. I went on to Qld Rail website and found all the details there including booking and paying for the tilt train. The airport train you pay at a booth just before boarding. Hope that helps Judy.
Judy, I wonder if your relative might be able to find a cheap flight from Brisbane to the nearest airport to Bowen. I've just checked my map. Townsville would be the closest, only 100 ks away from Bowen.