When you come out of the airport terminal, you head left towards the roundabout, where you have two options. Last April, I did a really silly thing and took the busy A-81 thinking it would be an easy way to access the camino. I spent an hour thrashing my way along behind the barrier with the constant roar of traffic before clamouring down through some undergrowth to get over a barbed wire fence onto the camino path. It was great fun..
Instead, I should have taken the road to the left, the N-643 which directly intersects the camino after a kilometre or so.. It's still a busy road but would be much safer! A couple of hours of very pleasant walking will get you to Muros de Nalón. It's a nice small town with plenty of places to eat. I haven't slept there, but gronze shows a few options. Both times I passed through it was busy with pilgrims, it seems a popular stop, so perhaps book your first night there.
... but if you do decide to take a bus, Aviles is a great town too, with a lovely historic centre. It's a much nicer place to start walking than Gijon.
Looking on Google maps, just now.. here's where the road intersects with the camino, it's less than a kilometre, more like 500m after the roundabout..
View attachment 165269