David,
First it would be a transfer to Rhoose village station for the once an hour service to Bridgend to connect with the mainline, on the other hand if the airport laid on a transfer to/from any of the four railway stations in Barry then there is a train every 15 minutes to connect with the mainline at Cardiff Central and/or up the valleys or to Brum and further north.
Perhaps that's part of the airport's mistake, for many a year the Rhoose line was freight only, they reopened it for a once an hour service, called it "Cardiff Airport" station when all the majority of train travellers want to do is get to Cardiff Central and they don't want to wait for up to an hour to do so and Barry rail station must be only about 3 miles, less than 10 minutes, from the airport.
There was a time when National Express served the airport, they had a codeshare on the Cardiff X91 Bus to connect with NE coaches at Cardiff Central, that clearly didn't work, then as I mentioned a couple of posts ago an independant (Llandow) bus operator specialised in the early morning and late evening services but that only seemed to work for bringing all the drunks home from the pubs.
The airport clearly need to get their transport sorted out because it seems they still haven't sorted it some 25 years since I started working at CWL.
Transferring to/from BHX? ... I was a regular, I'd park the car for free at Hampton-In-Arden rail station to take the 3 minute train ride into Birmingham International then a minute or so on "Pinky or Perky" listening to the most irritating BMI Baby jingles
, then down an escalator and I was at the check-in desk!!!