Rose bowl is always Big 10 Pac 10.
USED to be before the BCS and CFP.
If the Rose Bowl is not in the playoff process in a given year, yes it reverts back to B1G and Pac 12, but recent Rose Bowls:
Rose bowl prior to CFP (BCS era):
02 Nebraska-Miami
03 Washington State-Oklahoma
05 Texas-Meatchicken
06 USC-Texas
11 TCU-Wisconsin
Rose bowl as CFP playoff sites:
2015 Oregon-FSU
18 Georgia-OU
Since 2002, two Rose Bowls didn't even have either of B1G or Pac12 (2002 and 2018).
Edit: Also checked out this season's CFP, playoff sites are Orange and Cotton, with championship at Levi's at Santa Clara. Rose doesn't appear on any future selection for either playoff or championship games.
But, I think the fine print points out that the Rose Bowl is not committed to the old B1GvPac12 if either or both champions are in the CFP final four, allowing the Rose Bowl to go rogue and solicit any team they want. So, since unless the Pirate gets Wazzu into the final four, it's possibly the Pac 12 champ as one Rose Bowl team. If tOSU wins out or otherwise gets into the final four CFP (or even Meatchicken is B1G champ and final four selection), then apparently the Rose Bowl selection geezers are allowed to choose outside of the B1G on that side: thus Texas could be selected to play Wazzu if Wazzu is Pac12 champs but not final four, and B1G has a champ that IS selected for the final four.
Texas travels well ($$$$).