Linda I asked Spanish friends today about bike on the EA bus. All them told me never seen bikes on bus. And don’t think they are permitted on the EA
When I see the EA stopping at Prado (closest stop for San Sebastián bus Station) I never seen out side bike rack on front of the bus.
Or a one get off bus with bike.
It does get crowded at times when flights arrive.
Possibly you may have to wait on the next bus(buses) to put bike on.
Speaking of bikes on buses in Seville, I have never seen bikes on, or in, the city buses either.
I will post link to bike paths in Seville. They are all over the city. Green dedicated bike paths.
Seeing time you arrive and what you want to do, time wise you can do it. But will be bit of a rush.
Why not stay first night (I.e. at Hotel Simon or Tirana Backpackers).
If you don’t bike the Plata, then will have to catch bus from Plaza de Armas to italica and back to Seville.
Switching/ crossing over to Seville Este area will get you away from the crazy heavy traffic from the airport.