Károly and his brother have scored at the top level in several Mathematics and Physics competitions for high school and university students in Hungary.

Károly entered the Faculty of Science of the Eötvös Loránd University in Hungary, and completed his Diploma in Mathematics in 1978.

During 1978–2003, while being on a number of special leaves from Eötvös Loránd University, he has held numerous visiting positions at research institutions in Canada, Germany, the Netherlands, and United States.

Between 1998 and 2001 Bezdek was appointed a Széchenyi Professor of mathematics at Eötvös Loránd University, in Budapest, Hungary.

[6] His research interests are in combinatorial, computational, convex and discrete geometry including some aspects of geometric analysis, rigidity and optimization.

The conference proceedings "Discrete Geometry and Optimization", Fields Institute Communications, Springer, New York, 2013, edited jointly by him, Antoine Deza (McMaster University) and Yinyu Ye (Stanford University) reflects and stimulates the fruitful interplay between discrete geometry and optimization.