My 2nd great-grandmother is the Sarah Bean mentioned in your message.
I have spent quite a bit of time with the Botetourt Co records, including a visit there several years ago. I could find not any direct evidence to link Joseph Bean to either Joshua or Josiah Bean of that county. He served as bondsman for the marriage of one of Josiah Bean's daughters, leading many to conclude he was the son of Josiah Bean. However, Joseph is not listed among the heirs of Josiah Bean. There may be some familial relationship, but I have not personally explored it. Good luck.