How does Bradford change the structure of his narrative at the beginning of Chapter XI?
Well, first keep in mind that what you are referring to is the transition between the first book and the second book in what is usually referred to as Bradford's Of Plymouth Plantation. Where the first book is about the Reformation in Europe (and especially in England in regards to the Church of England) and what got the colonists on their way, the beginning of the second book is primarily about the possibility of new government in the new world. In chapter 11 (the first chapter of the second book), the structure changes specifically in reference to before leaving England vs. being en route to the new world.
In this eNotes Educator's opinion, the first book deals with philosophy and the second book, which starts with chapter 11, deals with government. The specific dates that are given for the first book are 1550-1607. Any scholar of New England history can tell you that is before the first settlement happened. The structure of this part of Bradford's "history," then, is truly about the philosophy behind the move. For example, much of it before chapter 11 is about what the people were fleeing:
[We were fleeing] the persecutions of the heathen and their emperors. ... For many endured sundry kinds of torment, often rackings and dismembering of their joints [as a result of their ideas].
In chapter 11 (the beginning of the second book), Bradford suddenly changes the structure by returning to specifics about the settlers still on the boat and before they land at Plymouth Rock.
In taking this different structural turn, Bradford begins speaking about the new possible government. The pilgrims on the Mayflower discussed their ideas of government as they traveled. In fact, they already had a government set up before reaching the New Land. Then again there were the "discontented and mutinous" strangers who ascertained that they would be free once they landed and not have to follow any rules of this new government. These "strangers" claimed "Virginia" as their own. The rest of the chapter is about the "New Government" of "New England" as proposed by the loyal subjects of James I of England.
In conclusion, the structural changes between chapters 10 and 11 are the structural changes conducive to the difference between books 1 and 2 in Of Plymouth Plantation. In short, these changes are about thoughts before the voyage vs. government plans during the voyage by boat to the New World.
At the end of Chapter X, Bradford begins to relate what he has to say in what he calls "annals," discussing what happened in each year, starting at the end of 1620. Each annal has a headline that simply states in which year he is writing. Previously, he had arranged his narrative in chapters that told the saga of the Pilgrims. Beginning with Chapter XI, Bradford relates the formation and signing of the Mayflower Compact at the end of 1620, and his account goes on to tell of the starvation the Pilgrims faced and the first Thanksgiving they celebrated. It ends in the year 1647-1648 (and also includes events that go up to 1650).
The structure of the earlier chapters, before Chapter XI, is based on a thematic narrative, in which Bradford believes that the Puritans are restoring true Christianity in a world overcome by Satan and that God supports them. In the later chapters, starting in Chapter XI, Bradford's writing lacks a narrative form and is more brief. While it is still clear that he believes the Pilgrims can achieve godliness, his account is mainly about how the Pilgrims establish a government and about their dealings with the Native Americans. The later chapters, which are encapsulated in Book Two, lack the narrative strand of God propelling them towards their destiny (present in the earlier chapters) and deal with more earthly matters related to their survival in the New World.