In August 2021, we took the bus from the Madrid airport to Astorga. Our Delta flight arrived at T-1 at 8:45. We had planned to take the shuttle bus to T-4, but we didn't realize that its schedule had been seriously curtailed because of the lack of incoming international flights due to COVID restrictions (and the fact that it was a Saturday). So we ended up taking a taxi to T-4. (It's quite a distance, by the way.) We had no trouble getting there on time. The ALSA buses arrive and depart from the bottom level of T-4. We bought our tickets online before leaving home. As has always been our experience with buses in Spain, the ride was comfortable (even though it was 104 degrees outside) and interesting.
In Astorga, the bus station is very nearly across the street from the cathedral so it is very convenient. We stayed at the Hotel Astur Plaza, which is on the plaza mayor near the government building and some interesting Roman ruins. It's a very nice hotel and a perfect location (right on the Camino). We arrived on Saturday afternoon and stayed until Monday morning. Sunday we went to mass at the cathedral and visited the Bishop's Palace, which was designed by Antonio Gaudi and contains the Museum of the Camino. We really enjoyed seeing a bit of Astorga before getting on the Camino. After all, we may never have another chance to see it!
Buen Camino!