He was known for sprinter's speed and long touchdown runs, but Bulaich was also the team's kicker, punter, and a safety on defense.

[3][4][5] After playing college football at Texas Christian University, Bulaich was selected in the first round (18th overall) in the 1970 NFL draft by the Baltimore Colts,[5] for whom he wore number 36.

[1] He was traded from the Colts to the Philadelphia Eagles for a 1973 fourth-round selection (83rd overall–Kansas lineman Gery Palmer) and a 1974 second-round pick (37th overall–Ed Shuttlesworth) on January 29, 1973.

[3][12] In 1974, Bulaich had been knocked unconscious when the Eagles played the St. Louis Cardinals in the first game of the season (September 15, 1974[13]), suffering a concussion.

[14] The Eagles sent Bulaich to Duke University Hospital, where the doctor recommended rest so the injury could heal, comparing it to a bruise.

[14] In August 1979, Shula was successful in convincing Bulaich to come out of retirement to play for the Dolphins as Larry Csonka's backup.

[16] Bulaich ultimately retired from the Dolphins later in 1979, after a play in which his face was crushed in an on-field collision with opposing players, resulting in broken facial bones and being unconscious for five minutes.