Exodus 4:31 And the people believed: and when they heard that the LORD had visited the children of Israel, and that he had looked upon their affliction, then they bowed their heads and worshipped.
They believed God. They saw that God was good to them. They were grateful. They bowed and thanked God. This is their worship.
As they remembered what God had done, they worshiped. They were grateful. They were recognizing God for being who He said He was.
Exodus 12:27 That ye shall say, It is the sacrifice of the LORD’s passover, who passed over the houses of the children of Israel in Egypt, when he smote the Egyptians, and delivered our houses. And the people bowed the head and worshipped.
The next time the word worship is used, they are only told where to worship.
Exodus 24:1 And he said unto Moses, Come up unto the LORD, thou, and Aaron, Nadab, and Abihu, and seventy of the elders of Israel; and worship ye afar off.
Then we see worship in a horrible sense. It is false worship or worshipping idols, false gods.
Exodus 32:8 They have turned aside quickly out of the way which I commanded them: they have made them a molten calf, and have worshipped it, and have sacrificed thereunto, and said, These be thy gods, O Israel, which have brought thee up out of the land of Egypt.
God next shows them His power and presence. They didn’t even come near. They worshiped in their tent door.
Exodus 33:10 And all the people saw the cloudy pillar stand at the tabernacle door: and all the people rose up and worshipped, every man in his tent door.
Worship is again bowing the head. It is humility before God. It recognizes God and His power.
Exodus 34:8 And Moses made haste, and bowed his head toward the earth, and worshipped.
God makes it clear that He wants no other deity acknowledged. He wants their worship. He never wants to see them worship another god.
Exodus 34:14 For thou shalt worship no other god: for the LORD, whose name is Jealous, is a jealous God: