With UCLA now 5-4 in the Pac-12, the Bruins are in sole possession of sixth place in the overall conference standings. With Stanford at 10-2 (8-1), and ranked No. 9 (likely moving up to 6-ish) in the CFP poll, the Cardinal is probably not in line for the Playoff.
Assuming Stanford beats USC, Stanford will go to the Rose Bowl. Now, the next three bowls in the bowl tie-in hierarchy can all drop down a level to take another school if they want to, but we can't imagine any of the bowls actually wanting to drop down to scoop up, say, UCLA. So, the top four bowls in the conference would shake out something like this:
Rose -- Stanford (8-1)
Alamo -- Oregon (7-2)
Holiday -- Washington State (6-3)
Foster Farms -- USC (6-3)
After the top four, bowls can no longer drop pick a team with a worse record -- they have to pick in order. This is key, because there's one more 6-3 team remaining before UCLA can be selected:
Sun Bowl -- Utah (6-3)
That leaves UCLA with the Las Vegas Bowl. Because UCLA is in sole possession of sixth place, and is the only 5-4 team in the conference, Most likely the Bruins would have to be selected there, regardless of the Vegas Bowl's preference.
The question is whether UCLA would accept. That's a remarkably early bowl game (Dec. 19th), and will come pretty quickly after UCLA's finals in the quarter system, which could limit practice time. Last year, we heard from someone at UCLA that they would have had to refuse the Vegas Bowl if offered for exactly that reason, so that's something to keep in mind. But we're also hearing from sources at UCLA that are indicating the Vegas Bowl might be the option this year.
If not, UCLA could go to the Cactus Bowl, which is Phoenix (Ariz.) on January 2nd.
If UCLA were to go to the Vegas Bowl, the opponents are either the Mountain West #1 or BYU. UCLA already played BYU this season, and while it's not out of the question that two non-conference oppoentns have a re-match in a bowl game, we think it would be more likely UCLA would face the winner of the Mountain West Championship Game (Dec. 5th), either San Diego State or Air Force. San Diego State is favored in the game.