I've never heard "Doze Bowl", but growing up in Florida, I'd watch the Citrus over the Rose. The Rose always came on at a weird time, like 4:00 or something like that.
My first bowl memories was the 10-9 CU-ND game where Rocket ran it back, but it didn't count. That same year (1990 season), living in Jacksonville, I recall Michigan running all over Ole Miss in the Gator Bowl.
In the '91 bowl season, I wanted Michigan to beat Washington, but my main memories are Bettis and ND running all over Florida in the Sugar that year.
The only Roses I remember really sitting down and watching were:
95 season - pulling for underdog Northwestern losing to USC
96 season - OSU beating ASU, making the Sugar the de facto NC game
01 season - NC game - Miami all over UNL
Since then, I'd say any playoff or NC games, but I don't remember #1 USC vs Michigan in the 03 season. I liked the Dayne games for Wisconsin, but I had no clue the Badgers beat UCLA 5 years earlier in the Rose as well.
Hmmph. Just a share.