Băjenaru began playing Go when he was 13 years old (1993). After just one year he rose to the rank of 1 dan.
After winning the Romanian Youth Championship twice he started to wonder if he'd ever be invited to study in Japan. Finally, when he met Kobayashi Chizu in Italy at the European Go Congress where he was finally offered the chance to become an Insei in Japan. In 1997 he moved to Japan. He played Ishida Yoshio for a Go magazine a mere month after moving to Japan.
Băjenaru was doing very well as an insei, promoting to class A. Due to these results and Kobayashi Chizu's help, Dragos was able to study with Japan's top player at the time, Cho Chikun. Dragos was very honored because at the time, Cho Chikun held the three top titles in Japan (Kisei, Meijin, and Honinbo). His best result as an insei was almost qualifying for the Honsen, which was where the top three players where promoted to professionals. He had scored 2 wins and 3 losses, just one win away from entering Honsen. After spending a year as an insei, Dragos decided to move back to Romania and finished his schooling. In 2005 he graduated from the University of Bucharest with a degree in Computer science. He currently works for Qubit Computers, which he co-owns.