The Rose and Cotton weren't part of it. The Cotton Bowl had higher ranked teams than the Fiesta in 1996.
Cotton had #5 BYU vs. #14 Kansas State, while the Fiesta had #7 Penn State vs. #20 Texas.
The Rose had #2 Arizona State vs. #4 Ohio State, while the Orange had #6 Nebraska vs. #10 Virginia Tech.
The Sugar, with #1 Florida State vs. #3 Florida, was the top Bowl that year.
The Rose Bowl crowned the National Champion the next season, when #1 Michigan beat #8 Washington State, 21-16.
The BCS started in 1998.