There was indeed a gristmill close to the bridge which it derived it's name from. People in and around Chesterhill don't know it by this name, they call it the Williams Bridge. Some accounts have the old mill standing into the 90's. Bryan Ketcham in his 1969 book only makes reference to it being there in "earlier days". Last year when I was there I could find no evidence of one. There was a house close by, and perhaps it was built on the foundation of the old mill.
Anthony Dillon takes very excellent pictures. The bridge is probably named from a mill that may have existed at one time. It would be a sweet research project to look up the history of the bridge. I would do it if I was near it.
Photos are beautiful. Does anyone know which Barkhurst the bridge was named for or any details about its history?