The answer to this, or at least hints about Zinn’s answer, can be found in Chapter 3 of the book. In that chapter, Zinn is discussing class conflicts in the American colonies. He clearly implies that he believes that it was historical forces, not free choice, that led European men and women to sign indentures.
From what Zinn says, we can infer that he thinks there were two main historical forces that drove white men and women to sign up to be indentured servants. The first of these forces was the beginning of capitalist commerce in England. Zinn talks about how this commerce drew poor people to cities where they tried to find work. Some of them were forced off the land that their families had lived on for centuries when landlords began to “enclose” their land, largely to raise sheep. As he says,
In England, the development of commerce and capitalism in the 1500s and 1600s, the enclosing of land for the production of wool, filled the cities with vagrant poor…
These poor people had very few options, leading many to sign on as indentured servants.
The second historical force was the demand for labor in the New World. Because so much labor was needed, landowners in the New World would pay well for indentured servants. This, Zinn says, created a situation where people could make a big profit by recruiting and shipping indentured servants.
Thus, Zinn implies that it was historical forces that drove European men and women to sign indentures.