After attending Liberty University, Bream was drafted by the Dodgers in 1981. Though thrice ranking among the minor league home run leaders, he batted no higher than .184 in limited playing time before getting traded to the Pirates in 1985. In Pittsburgh, he regularly played over 100 games a year for the Pirates, hitting at least 10 home runs in four full seasons (1986–88, 1990) with them. Defensively, he set an NL record for most assists in a season with 166 in 1986. After a knee injury cost him most of the 1989 season, he hit 15 home runs in 1990 as the Pirates reached the playoffs, losing to the Cincinnati Reds in the NLCS.