Airport bus to Atocha Stn. ?where exactly is the arrival pont?

Edited to add: WARNING--Priscilla's information about the location of the bus drop-off point is probably more accurate than mine!

I was brain-dead and jet-lagged when I took the airport bus to Atocha this summer. I don't remember where it dropped me off beyond a vague recollection of being down the right side of the building (from the perspective of someone walking out of Atocha toward the traffic circle).

This website has a map with the bus drop-off marked. I assume the location hasn't changed but cannot guarantee it. It's not inside the station. The website also gives a bit of information about how to find the bus outside the airport terminal. That may be helpful as well.

The area around Atocha is quite open; you don't walk right outside and see street signs. It took me some minutes to get oriented and figure out the correct direction for my hotel. It was helpful to have an electronic map on my phone that pinpointed my location using GPS without depending on cell-phone service (which I did not have). If you're traveling with a smartphone or tablet, I recommended loading one of the apps that works without Wi-Fi and cell reception once you've loaded the basic app and the appropriate maps. I use CityMaps2GoPro, but there are others.

I did not take the bus back to the airport and do not know whether the pick-up point is exactly the same as the drop-off point.

S,

We took the Cercanias train (C-1 line) from the airport (Terminal 4) directly to Puerta de Atocha train station because we were connecting to an AVE train to Córdoba.

Since you plan to take the Airport Express bus. The bus arrives here, in front of the Atocha station, on Paseo de la Infanta Isabel.

If you check the satellite view, you'll see a large circular structure with red columns, the bus stops, in front of the structure, you can even see a bus on this view.

Have a great trip!

Edited to correct... I tried to clarify my original post.

Thank you both!
That info is extremely helpful.
I can even see where you can pick up a taxi across the street from the bus drop off.
Do you know if the bus back from the station to the airport goes from the same stop?
I've never been to Madrid before, so really looking forward to it!

S, Jackson,
I believe the bus departs ( back to the airport) from the same location, but it's best to ask the bus driver upon your arrival & he/she will point where the stop is.
As aforementioned, we didn't take this bus to Atocha. We took the Cercanias C-1 line to/from Atocha to/from the airport (Terminal 4)

Enjoy Spain!

Thank you all. The bus was v. Convenient , and stops and leaves exactly as you all had said.

Thanks for the update!
Enjoy Spain!