Bipartisanship involves two political parties or factions working together to get things done. It can take a lot of skill to convince two parties that normally are rivals to work toward a common goal.
The prefix bi- at the beginning of bipartisanship means that two things are involved. Drop the prefix and you have partisanship, very much the opposite in meaning. Partisanship involves supporting the views and policies of just one political party, no matter what. In contrast, bipartisanship involves compromise between political parties that often have opposing views. Bipartisanship is a relatively new word that reflects the growing importance of exploring ways to overcome strong political disagreements.