Moses goes up and down the mountain at least five times that I counted.
-Tim-
Starting from the time the Israelites arrived at Sinai:
Exodus 19:2-8a: There Israel encamped before the mountain, while Moses went up to God (…) So Moses came and called the elders of the people and set before them all these words that the LORD had commanded him. All the people answered together and said, “All that the LORD has spoken we will do.”
Exodus 19:8-b-15: And Moses reported the words of the people to the LORD. And the LORD said to Moses (…) Moses told the words of the people to the LORD (…) So Moses went down from the mountain to the people and consecrated the people; and they washed their garments. And he said to the people, “Be ready for the third day; do not go near a woman.”
Exodus 19:19-20:20: And as the sound of the trumpet grew louder and louder, Moses spoke, and God answered him in thunder. The LORD came down on Mount Sinai, to the top of the mountain. And the LORD called Moses to the top of the mountain, and Moses went up. (…) And the LORD said to him, “Go down, and come up bringing Aaron with you. But do not let the priests and the people break through to come up to the LORD, lest he break out against them.” So Moses went down to the people and told them. And God spoke all these words, saying, “I am the LORD your God, who brought you out of the land of Egypt, out of the house of slavery. (…)” Now when all the people saw the thunder and the flashes of lightning and the sound of the trumpet and the mountain smoking, the people were afraid and trembled, and they stood far off and said to Moses, “You speak to us, and we will listen; but do not let God speak to us, lest we die.” Moses said to the people, “Do not fear, for God has come to test you, that the fear of him may be before you, that you may not sin.”
Exodus 20:21-24:8 The people stood far off, while Moses drew near to the thick darkness where God was. (…) Then he said to Moses, “Come up to the LORD, you and Aaron, Nadab, and Abihu, and seventy of the elders of Israel, and worship from afar. Moses alone shall come near to the LORD, but the others shall not come near, and the people shall not come up with him.” Moses came and told the people all the words of the LORD and all the rules. And all the people answered with one voice and said, “All the words that the LORD has spoken we will do.” (…)
Exodus 24:9-11: Then Moses and Aaron, Nadab, and Abihu, and seventy of the elders of Israel went up, and they saw the God of Israel. There was under his feet as it were a pavement of sapphire stone, like the very heaven for clearness. And he did not lay his hand on the chief men of the people of Israel; they beheld God, and ate and drank.
Exodus 24:12-32:16: The LORD said to Moses, “Come up to me on the mountain and wait there, that I may give you the tablets of stone, with the law and the commandment, which I have written for their instruction.” So Moses rose with his assistant Joshua, and Moses went up into the mountain of God. And he said to the elders, “Wait here for us until we return to you. And behold, Aaron and Hur are with you. Whoever has a dispute, let him go to them.”
Then Moses went up on the mountain, and the cloud covered the mountain. The glory of the LORD dwelt on Mount Sinai, and the cloud covered it six days. And on the seventh day he called to Moses out of the midst of the cloud. Now the appearance of the glory of the LORD was like a devouring fire on the top of the mountain in the sight of the people of Israel. Moses entered the cloud and went up on the mountain. And Moses was on the mountain forty days and forty nights.
And he gave to Moses, when he had finished speaking with him on Mount Sinai, the two tablets of the testimony, tablets of stone, written with the finger of God. (…) Then Moses turned and went down from the mountain with the two tablets of the testimony in his hand, tablets that were written on both sides; on the front and on the back they were written. The tablets were the work of God, and the writing was the writing of God, engraved on the tablets.
Exodus 34:1-29: The LORD said to Moses, “Cut for yourself two tablets of stone like the first, and I will write on the tablets the words that were on the first tablets, which you broke. Be ready by the morning, and come up in the morning to Mount Sinai, and present yourself there to me on the top of the mountain. No one shall come up with you, and let no one be seen throughout all the mountain. Let no flocks or herds graze opposite that mountain.” So Moses cut two tablets of stone like the first. And he rose early in the morning and went up on Mount Sinai, as the LORD had commanded him, and took in his hand two tablets of stone. The LORD descended in the cloud and stood with him there, and proclaimed the name of the LORD. (…) When Moses came down from Mount Sinai, with the two tablets of the testimony in his hand as he came down from the mountain, Moses did not know that the skin of his face shone because he had been talking with God.