According to google, there is an ALSA bus at 4.30, 5.30 and 6.45 on a Sunday, direct to Oviedo. When I caught the bus from Oviedo to Bilbao in May this year, we called in at Santander but I did not need to change. It cost 34 Euros and the bus was supremely comfortable. I have yet to check, but I think that ALSA used a different name for Oviedo in the timetable.
The Primitivo is a lovely route. There's a good hill a day to climb but if you're fit(ish) it's not too bad. I'm in my 60s and had no problems at all. There was a couple doing the route in 15km stages because the wife had knee problems. However, if you can walk the SW coastal path, with all its ups and downs, you will have no problems with the Primitivo.
I agree that you might as well walk the SW coastal path as walk the Norte. Similar scenery, excellent food especially fish. Probably quite a lot more expensive to do though. I gather there is quite a bit of road walking on the Norte - that's one real advantage of the SWCP with our wonderful paths right next to the sea. When I walked from Murxia to Finnisterre I was frustrated by the amount of road walking and the lack of coastal path.