Born in Portsmouth, England, the son of a marble cutter, Bonfield emigrated to America with his family in 1816. He settled in Philadelphia where, while working at the estate of Napoleon Bonaparte's exiled brother, Joseph Bonaparte, was encouraged by the French ex-patriot to begin a painting career.
A painting exhibited by Bonfield at the Pennsylvania Academy of Fine Arts in 1820 prompted the academy's president to arrange for Bonfield to study marine and landscape painting there under Thomas Vest. The artist would spend the rest of his life in Philadelphia, creating quality shipping scenes. He was considered one of the leading marine painters in America during the early part of the 19th century.
Bonfield was an early member of the Pennsylvania Academy. He exhibited there between 1847 and 1867 as well as the Artist's Friends Society (1836-45), the National Gallery (1837-44) and the Maryland Historical Society (1848). He is known to have traveled widely as backgrounds for his paintings include both England and France, as well as locations in Pennsylvania, Massachusetts, Rhode Island and New York.