Bok was born in the small Dutch town of Hoorn, north of Amsterdam, to Jan Bok, who was a sergeant-major in the Dutch army, and Gesina Annetta (née van der Lee) Bok, but he spent a good deal of his childhood with his grandparents in the town of Haarlem, where he attended primary school. He attended high school in The Hague, excelling at mathematics and science, and he also told the story that this was where he met a Scoutmaster who introduced him to the night sky while on camping trips away from the city lights. After completing high school, he went on to study astronomy at Leiden and Groningen Universities.