Born and raised in the Bay Area of California, Bryggman attended the City College of San Francisco before heading to New York, where he made his Off-Broadway debut in "Summer Ghost" (1962). After stints with the Pittsburgh Playhouse and in Boston, he began his long association with Joseph Papp's New York Shakespeare Festival (NYSF) with 1969's "Mod Donna" and over the course of nearly three decades played numerous roles in the canon, including Banquo in "Macbeth" and the title parts in "Coriolanus" and both parts of "Henry IV". Alongside Pacino, Bryggman appeared in "The Basic Training of Pavlo Hummel" (1977) and "Richard III" (1979). Bryggman segued to the big screen in support of Pacino in the legal drama "... And Justice for All" (1979) and enjoyed his most prominent role as a policeman sparring with Bruce Willis' John McClane in "Die Hard With a Vengeance" (1995).