Do not know how much luggage with you, but if it is your rucksack, I would recommend taking the airport bus into La Coruna, spending some time there, having lunch (seafood is very fresh, as has been landed that morning), and catching the train (maybe the 14.31 or 15.05) in the afternoon to Ferrol. A Coruna has so much more to offer than Ferrol, and there is a huge choice of restaurants in the old city and on the promenade facing the port. In addition, restaurants in Ferrol do not open for dinner until 8pm -8.30pm, and therefore after a long travel when you just need an early dinner and bed ready for beginning walking, it is nigh impossible to do in Ferrol,, unless you either go to the McDonalds or go to bed hungry.
The airport bus does pass both the bus and train stations at A Coruna. The bus stop for both is the one after the bus has stopped opposite a very large Carrefour supermarket. For the bus station just carry on up the embankment on the side of the road where the bus stop is. For the railway station, go over the dual carriageway on the pedestrian footbridge, then up the hill and you will see the railway station the other side of the roundabout.
Although the train takes twice as long as the bus, I prefer the train firstly for security reasons, as you have your luggage in your sight, instead of it being in a hold down below, and you do not have to fret every time the bus stops whether someone has walked off with your luggage - it has been known to happen. Secondly, after Betanzos, the railway essentially does the first two days of the Ingles in reverse, so you have a good chance to see where you are going to walk. You can also see the two short cuts over the N-651 bridge and on the footpath by the railway bridge, if you are walking all the way to Pontedueme on the first day.
There are local buses which go from La Coruna city centre to the railway station, but you really need to know where to get off. If you ventured into the centre, I would recommend either taking a taxi for the short distance to the railway station, or taking the airport bus (basically get off on the first stop on the dual carriageway road once you have turned away from the port. It will also be the stop that lots of people get on the bus with their suitcase. Walk in reverse for 50 metres, then follow the footpath up the slope on the left, and carry on up the street to the roundabout which you cross over.
No need to arrive at the railway station more than 20 minutes before the train departs. There are no queues, especially in mid afternoon. The ticket machines have an English language option, and there are plenty of seats on the train, so do not worry that you need to book in advance or that there will be no seat.
@davebugg, on the basis that a taxi fare from La Coruna airport to the centre of La Coruna cost me some € 40, a taxi from La Coruna airport to Ferrol will likely cost a fortune. As to fellow pilgrims being on the flight from Madrid, you will be very lucky to see any. The Ingles is very lightly walked, especially in October. I saw no more than 10 pilgrims per day on the Ingles, and that was in Holy Week