Bryce was born in Evanston, Illinois in 1954. He is a 1976 graduate of Stanford University, and received his law degree from the University of Chicago in 1979. He was a Law Clerk to U.S. Supreme Court Justice William Brennan, and Legislative Counsel to Alan Dixon, a U.S. Senator from Illinois.
He practiced law in Chicago from 1982 to 1998. Bryce served on the Finance Committee for Harold Washington's campaign for Mayor in 1983, and on Paul Simon's successful campaign to unseat Charles Percy in the 1984 U.S. Senate race. He was the Finance Chairman for Richard Daley's campaign for Mayor of Chicago in 1989. From 1991 to 1994, he was the Finance Chairman of the Illinois Democratic Party. He was an unsuccesful candidate for Attorney General of Illinois in 1994.
Bryce was the National Finance Chairman of Jed Bartlet's campaign for the Democratic presidential nomination in 1998.