Charles Ellicott Commentary Exodus 34:33

"And when Moses had done speaking with them, he put a veil on his face." — Exodus 34:33 (ASV)

Till Moses had done speaking with them, he put a vail on his face. —This translation exactly inverts the meaning, which is that when Moses had done speaking with them, he put a vail on his face. The veil became part of his ordinary costume, and was worn except on occasions of two kinds:

1. When Moses was alone with God, either in the temporary Tent of Meeting or in the permanent Tabernacle, he ceased to wear the veil, and spoke with God face to face;
2. When he had a message to the people from God, and spoke to them as God’s representative, he authenticated his message by uncovering himself, and allowing the glory of his face to be seen.

Otherwise, in his ordinary dealings with the people he went about veiled.