Answer:
The statement is false. William Bradford wasn't the first governor of the Massachusetts Bay Colony, but John Carver.
Explanation:
John Carver was a Pilgrim leader and the first governor of the Plymouth Colony.
John Carver was probably born in Nottinghamshire, England. He was a wealthy merchant who had amassed his fortune in London with trade but who, like many contemporaries, left his country to escape religious persecution. He traveled to the then relatively safe Netherlands and arrived with a small group via Amsterdam in Leiden in 1607 or 1608.
From there he followed the religious developments in his home country, but as the years passed he foresaw more future for himself in the New World.
In 1617, he acted for a group of like-minded believers, later known as the Pilgrim Fathers, as a negotiator in chartering the Mayflower and raising funds to found a colony in the New World. With the "Mayflower" and 101 other settlers, he sailed in September 1620 from Plymouth to the new world. On November 11, 1620, together with 41 other people on board, he signed the so-called "Mayflower Compact". The document was nothing more than a simple set of regulations to make the colony landing and foundation possible. That same day he was chosen by the Pilgrims as governor for a year of the "Plymouth Colony", also called "New Plymouth" or "The Old Colony".
During the first winter, many settlers died as a result of poor living conditions, but also due to illnesses and malnutrition.
John Carver himself died in the spring of 1621, reportedly due to heat stroke. He was succeeded by William Bradford.