I am descended from William Bamber's sister Elizabeth Bamber. She married Thomas Tomlinson and they had five children. After Thomas Tomlinson died in 1822, Elizabeth and her children came to the United States in 1829. They settled in Brown County, Ohio to be near William Bamber and his wife Elizabeth Crombleholme. When William Bamber died in 1833. Elizabeth Bamber Tomlinson and her younger children moved to Monroe County, Illinois to live near her brother (and William's brother) John Bamber and his wife Ellen Walker.
I have visited Brown County and was able to locate the grave of William Bamber and also the grave of Elizabeth Crombleholme Bamber. I have some information on the Bamber and Crombleholme families in Lancashire if you are interested.