I cannot say if we are related to your Bunn branch, as I don't know too much about our branch. I have found them living in Suffolk England around the late 1700-1850's then I can't find any others, as it is a 4 or 5 times Great Grandmother wo was called Rachael Bunn, if you think your Bunn relatives came from Suffolk, I can dig in my files a bit deeper and see if I can find a connection,
Regards,
sue Button