We are flying into Madrid's Barajas airport in late October. We arrive at Terminal 4S on a flight from Morocco. Do you know where the pickup point is for the shuttle vans that could take us to a hotel?
You can get the Aero City van in Terminal 1. I don't know if they also have desks in other terminals.
Check the Aerocity van service site. That should give you the information. I think there is a shuttle between the various terminals but have not used it. Also there is a Metro bus line to T 4 (and the other terminals as well) that goes into the city. It makes only three stops, but maybe one is near your hotel. Or get a taxi from that location. The metor is 5 euro per person. The location is well marked.
From the Aerocity website, the T4 pickup location is "T4 - Arrivals, to the right of the exit 10, at the end of the corridor once passed the coffee shop." You'll have to go from 4S to 4 first. The Aerobus is cheaper(5 euro) and runs every 20 minutes, with pickup outside T4. Depending where your hotel is, this may work for you.