I have read that the new airport bus is up and running. Here is a report from another travel forum, posted on Nov. 7:
"Yes! The Airport Express is running. I took it yesterday from the Atocha-Renfe station. It leaves every 15 minutes Monday to Friday, and every 20 minutes on weekends and holidays. It costs 2€ and took about 30 minutes with little traffic.
The stop at Atocha is just outside the round Cercanias building on the upper street level. This is at the easterly side of the main station above where the Cercanias platforms are. Take the escalators to top. The stop is marked by a vertical yellow sign. Pay the driver.
They're new bright yellow buses and have plenty of space for luggage on board (not underneath) and seating for a couple dozen people with lots of standing space.
It makes two other quick stops (Plaza de Cibeles and O'Donnell) before getting to the airport. It makes three stops at the airport: Terminal 1 departures, Terminal 2 departures and Terminal 4. At Terminal 4, the stop is at the upper arrivals level, so you have to take the elevator or escalators. It runs to and from Atocha between 6:00 AM and 11:30 PM. Between 11:30 and 6:00 AM, it only goes as far as Plaza de Cibeles.
It was fast, efficient and couldn't be any handier - or cheaper."