I did read, in the Spanish version, that the hospital where she was taken in had developed protocols for dealing with Ebola after it had to deal with a sick African found in a bus station in Madrid. She turned out not to have Ebola, but they were smart enough to develop a procedure, and apparently they applied it immediately to the Spanish nurse when she showed up. (Immediate isolation and disinfection is, of course, a big part of it.)
Amazing to me...I just expected much more from supposed civilized medicine.