Bloore was born in Brampton, Ontario, in May of 1925. He received a Bachelors degree in art and archeology from the University of Toronto in 1949. After his studies in Toronto, Bloore traveled to New York City, where he studied art history and archeology. From 1951 to 1954, he was also an Instructor in the art and archaeology department at Washington University. From 1955 to 1957, he studied at the Courtauld Institute of Art, at the University of London.
After his studies in London, Bloore moved back to Canada and became an instructor in art and archeology at the University of Toronto. He then moved west, to Saskatchewan. Bloore became a professor of art and archeology at the University of Regina in Saskatchewan and was a member of the influential abstract painting group, the Regina Five. Bloore moved back to Toronto in 1966, where he was a Professor in the Faculty of Fine Arts at York University until 1990.
In 1993, Bloore was made a member of the Order of Canada. Later that year, he was awarded an honorary Doctor of Letters degree from York University. In 2001, he was made an honorary Doctor of Laws by the University of Regina.