The phrase "bipartisan fashion" means that people from different political parties or viewpoints are working together and cooperating to reach a common goal or make a decision. Full definition
There also is a perception that women tend to work in bipartisan fashion more often than men — both inside and outside the legislative chambers. (timesunion.com)
He should also provide real leadership in getting an ESEA revamp across the finish line by embracing the bill that the Senate already passed in overwhelmingly bipartisan fashion. (educationnext.org)