NCAA bylaws state that only teams who "have an equal or greater number of wins than losses" can qualify for a bowl. A team can have a losing record and go to a bowl only if they are the conference champion, and only if the NCAA votes to grant a waiver.
With Stanfurd's win over Notre Dame, they may go to the BCS. If Oregon wins next week, UCLA will be 6-7 and ineligible for a bowl. The likely bowl selections are:
Rose - Oregon
BCS - Stanfurd
Alamo - Washington
Holiday - Cal *
Sun - Arizona State **
Vegas - Utah **
* The Holiday could pick Cal, Utah, or Arizona State. Cal has provided excellent attendance at Holiday Bowls in the past and is the logical choice geographically.
** The Sun Bowl would want Arizona State, as they are the best choice geographically. Ditto for the Vegas Bowl and Utah.
There would be no additional Pac-12 teams that are eligible.