Statement 1 is Correct: Bahrain is an island nation situated entirely within the Persian Gulf. The Strait of Hormuz is the only sea passage connecting the Persian Gulf to the Gulf of Oman and the open ocean. Therefore, for a ship departing from Bahrain to reach the Indian Ocean, it must exit the Persian Gulf by passing through this strait.

Statement 2 is Incorrect: Syria is located on the eastern coast of the Mediterranean Sea and has no coastline on the Persian Gulf. Ships departing from Syria would reach the Indian Ocean by traveling through the Suez Canal, down the Red Sea, and out through the Bab el-Mandeb Strait, completely bypassing the Strait of Hormuz.

Statement 3 is Correct: Qatar is a peninsular country located on the northeastern coast of the Arabian Peninsula, surrounded by the waters of the Persian Gulf. Like Bahrain, its ships must cross the Strait of Hormuz to access the Indian Ocean.

Statement 4 is Incorrect: Egypt borders the Mediterranean Sea to the north and the Red Sea to the east. Ships from Egypt can access the Indian Ocean directly by sailing south through the Red Sea and the Bab el-Mandeb Strait, without entering the Persian Gulf or crossing the Strait of Hormuz.

Therefore, the correct option is B.