Bajenaru was born in Pomona, California) and graduated from Ruben S. Ayala High School in Chino Hills. He began his college career at the Riverside Community College. The Oakland Athletics drafted him in the 13th round after his sophomore season, but he elected not to sign. He parlayed his community college performance into a scholarship at the University of Oklahoma. The Chicago White Sox chose him in the 36th round the next year, but he again returned to school. In 2000, he hit .342 with 11 HR's and 58 RBI. On the mound he was 1-2 with 20 saves (setting a conference and Oklahoma record for season and career) and a 2.62 ERA. He was a first-team college All-American as a utility player, and was a 1st Team Big 12 Conference selection as an outfielder and 2nd Team Big 12 Conference selection as a relief pitcher.