If a 1996 Chevy Cavalier is over heating even after the water pump etc was replaced and the system was bled could it be a bad water pump?

Overheating can be caused by a blown head gasket or cracked head. Blown head gaskets are quite common on newer four cylinder American cars.

Your radiador core can be blocked or radiator grille dirty and resricted , thermostat faulty , radiator cap not maintaining proper pressure .

Check to see if cooling fan on radiator is turning when car is in operating temp, or if air conditioner is on. If it is not turning it may have a burnt motor or bad relay. Try a jumper wire to test fan motor.