What was the source of the water used to fill the bronze sea?

Answer:

The Bible doesn't mention what water was used to fill the bronze sea. Jerusalem had numerous pools and we know from archeology that Solomon has several underground cisterns hewn into the rock. Ecclesiastes 2:6 mentions that Solomon did build pools. Any of these could have been used. See the Hasmonean Aqueduct for one water delivery system near the Temple mount.