I'm also doing some Bedwell genealogy research on the Squire Bedwell that you're researching. You've probably seen some of the same things that I've found. Squire's son, Leroy Calvin Bedwell (Rufus' brother), and grandson, Robert Louis Bedwell, are buried in the Mountain Spring Cemetery near Old Coloma, Cherokee Co AL. Since about half of the graves in that cemetery are unmarked, it's possible that they are also buried there. Alternatively, he may have been buried on his land in township 11S and range 10E section 32 of the Huntsville meridian.
By the way, there were also members of the Pace family and White family who were intermarried in that same neighborhood. I'm pretty sure that your husband's grandfather, Pace White Bedwell, was probably named after those families. Good luck with your search. Mike