How did the holy bible lead to modern science?

People became educated, and strayed away from Bronze Age dogma.

Step away from tunnel vision, this is a big world. Some scientists have never even read the Bible and not every scientist is Christian. So many have other beliefs that they practice and don't reject God, while Christians seem conflicted.

I'm not sure your premise is correct about the Bible leading to science. However, the Catholic Church stopping it's belief that the Bible must be accepted as literal truth was a step in this direction though. 

The invention of moveable type helped to make the Bible available to the masses for the first time. Once the masses were able to read the Bible, the meaning and interpretation previously abridged by the clergy to suit it's purpose of control, they learned what a crock it was. As such, it was inevitable that modern science was soon to follow.

Obviously the Bible's ideology and philosophy hasn't done that good of a job reducing superstition. There are still hundreds of millions of people who still worship, revere, and fear the supernatural entity that the Bible proffers.

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