If Iowa beats Michigan in the B10 championship game, Iowa goes to the Rise Bowl (unless they somehow ended up in the Top 4).

If Michigan beats Iowa, then whichever is ranked higher out of Iowa and Ohio State will go to the Rose Bowl (almost certainly would be Ohio State with only 2 losses versus Iowa's 3).

The Bowls don't really have a say in which teams go to which bowls, it's formulaic.  There is a tiny bit of input used in a couple of bowls that don't have a specific conference tie in if they aren't one of the CFB semi-finals (ie Peach, Fiesta, Cotton). In these cases they'll make an attempt to get the best matchup among the teams that have qualified for the NY6, but the CFP rankings decide which teams go to the NY6 bowls and, for the most part which teams play in which bowls.