OP, what you need to find is a reputable book conservator. You do not want a commercial bookbinder.
Agreed that the local library is probably your best bet for a local lead on a conservator, or you may want to contact your closest university library for information.
If you are having problems finding a conservator, as an interim measure you can have an acid-free cardboard box made for your bible, and use natural coloured cotton tape to tie the bible securely inside the box. The box will protect your bible from further damage due to light, dust and handling. Simpler still, you can purchase natural coloured acid-free paper and make a book cover (the type of cover we all used to make for books in grade school) with the paper, and tie up the bible securely with natural coloured cotton tape.
If a there is a community college near you where they teach archival studies, you may be able to hire a student to make a custom box for your family bible.
