The blood banks were slow to start screening donors for HIV because the correlation had not yet be made between the connection of HIV transmission through the donation of blood products until almost three years after the first cases were reported. When the first cases broke out circa 1981, it took a lot of happening for it to be decided that it was a blood-borne pathogen that could be transmitted. As of that point, it was thought of that only homosexual males were carriers of the disease.
It was almost 2-3 years until new and diverse cases began to be looked at with more clarity. This happened, for example when the patients diversified and were not only homosexual males but also drug patients addicted to needle drugs. After that children and women became victims as well and that's when the connection was finally made. So, in all, it was a combination of lack of knowledge with lack of evidence that would conclude that there was a need for screening.