Hi Sandy,
Thanks for clarifying your tree. I spent some time soing some research on Alexander Graham Bell's tree (thanks for posting that one Kirsty) to see where the connection with the Canonbie Bells might be, and I haven't found anything yet.
Yes, Kirsty you are right, there are a lot of Bells in Rowanburn.

I have some doubts about the AGBell connection though, as online trees have his Bell ancestors originating in Edinburgh and going back through generations in Fife and St Andrews whereas ours are in Dumfires as far back as we know.
I realise that "aunt" could mean cousin or other distant relative, but unless we find one of our Bells on the East coast or one of their Bells on the west coast, I'm afraid I think there may have been a mix up somewhere. You only ned to search the IGI for Alexander Bell born any date and there are huge numbers of them. And of course the middle name of Graham was added when he was older.
However I will keep looking. I haven't done much research of siblings of the direct ancestors so perhaps one of them connects somewhere, though they all appear to be very humble folks, so I have my doubts.
My Francis Bell was chr 1768 in Lymiecleugh.

The family lived in the Canonbie area for generations. Kirsty is correct - you should check as much as you can yourself. On the IGI several of the children born to Francis Bell and Margaret Nichol are submitted records (your Adam is one such submitted christening). As they are not my direct line I have put question marks beside their names as something to investigate further, however they do have full dates so are probably accurate.
There are dozens of posts on rootschat where people are trying to prove family rumours of links to famous people - sometimes the rumour is proven true, but often not.

Your ggrandfather may have been told and truly believed there was a link to AG Bell and passed on the information in good faith to his neice, but it still unfortunately may not be true.