there are 13 bishops in the entire game, and when one "retires" (dies, turns heretic, gets elected to popedom, etc.), the game picks a new one through the best non-bishop priests in the catholic factions. the more you have piety 5+ priests, the more you have a chance of getting one.

for the papal elections, there are 3 "preferati" that every catholic faction gets to vote for when the pope dies. these 3 preferati are the 3 highest piety bishops. Then, everyone votes, and the one with the most votes win. you can obviously rig the election, and you always vote for your own bishop.