It looks from the lack of responses as if no one is interested. I'd just like to make clear that this is not the case - we all dream of such a post as this about our own family. Also, anyone here would be happy to caretake such a bible, but hopefully you are equally happy to caretake until a descendant is found?
I think everyone is just waiting to give a member of the family itself time to see this message and respond. I'd guess this is also why no one has 'Answered' but simply commented - more people will read it as an unanswered question.
You may find other records throughout the library with personal names or dedications in them. It sounds wonderful.
Also, if you find a descendant to pass the bible on to, it would be lovely if you could then post again to let us know. It's always a happy story when an heirloom finds it's rightful place.