You can go by train, changing at Betanzos or Ourense which is around 7 hours (not great on Sunday, though)
Or Bus via Oviedo then train
Or train to Ponferrada, short walk to the bus staion then train (this looks like the fastest journey and also the cheapest but the times would have to fit as the bus is at 05:15 on weekdays. Might work if you stayed overnight in Ponferrada)
I found these on Rome2rio
Personally I would get the direct train to A Coruna and either get off in Santiago then get the train to Ferrol, or the bus, which you can get from Santiago (or go to A Coruna and bus from there) The Santiago bus station is a fairish way from the railway station. This option for some strange reason doesn't appear on either trainline or Rome2Rio, you have to look it up as two separate journeys. I haven't bothered with the RENFE site. Bear in mind the timetables change around now, so you will in any case need to look nearish to your journey time. If you happen to be over 60 you can buy a tarjeta dorada for cheaper train travel. You can buy it at the same time as your ticket You need to show your passport for proof of age and it costs about 6 euros. You can't use this with some promo fares.