Museum curator here: The best possible means of preservation would be to give it to a museum with an on site restauration expert who specializes in books. You go home with a few dollars or a nice tax deduction, knowing your bible is in good hands. Some museums evennoffer special permanent loan shemes where you retain legal ownership of your objects in return for the right to study and exhibit them.

If you don't want to do this (which is a legitimate course if action) or you get turned down by the museums (condition too bad / bibles are not what they collect / they already have a similar object), you could turn to a freelance restaurateur. Liok for credentials like "trained at <prestigious institution like Smithsonian>" or "worked with <multiple museums> before". They might charge you a hefty price though. Since what you describe seems to be an already strongly damaged book, you might want to ask someone straight out of art school/traineeship, they usually charge less and are happy to build their portfolio.

If you don't have that kind of money, I would advise you to take the book out of the tupperware container asap. Long story short: Humidity builds up quickly in plastic containers, which is detrimental for paper objects. Also, tupperware contains plasticiser, which is a chemical reagent that interacts with glue and ink and can further damage the book over time. Wrap the book in Glassine paper and store it in an acid free catridge box in a low humidity environment, out of direct sunlight and a little below average room temperature.

This is not the place to have an antique book's value assessed. But, generally speaking, there are many 19th c. bibles, so they usually aren't rare. Books in poor condition are also not worth much, much less than books in good condition. Do not be surprised if a museum or book dealer gives it a very low value and discourages restoration. However, old bibles often have important family or other information on the blank leaves, and those very definitely are worth preserving. As stated above, keeping them in an acid-free box at low humidity and at a cool temperature is a good thing to do, unless and until a paper conservator works on them.

Archivist here! Just to build on the other comment from a museum curator, you might consider seeing if there are archives in your area that would be interested in the book, or might at least be able to take a look at it and give you some guidance. You'd want to think about places that might have an interest in religious texts, the Civil War, or that have some connection to your ancestor. If you do want to see about getting conversation treatments on your own, the American Institute for Conservation has a conservator lookup, though based on what you're describing I'd guess you'd be looking at a pretty hefty bill. I'd also highly recommend the Northeast Document Conservation Center - they're extremely good at what they do, and in my experience they tend to be pretty generous with answering questions. Their website has a lot of excellent resources too if you're generally curious about conservation.

I hope this post is not taken down and I do not mean to inspire an argument, but I only mean to offer the flip side to the curator and archivist’s post here.

You can pay a conservator to fix your book, setting it up for a century of longevity, and keep it. Value is a subjective thing, right. Odds are this book is more valuable to you and your family (and the efforts of those family members who have passed down the book for over a hundred years) than it is to a library where it’ll get conserved but go on a shelf for maybe one person to pull in the next hundred years. A MAJOR point of contention with donation to institutions is that things go into storage, are never used, and in some cases can even be resold later on. All I’m saying is that you may consider the value of keeping it in your family, and it’s not a selfish decision to do so.

Unless it's 18th rather than 19th century (which it sounds like it isn't, as a civil war bible) it's ulikely to have much financial or historical value - it's much more meaningul as an heirloom.

Getting it restored will cost a lot of money but you might enjoy owning it like that.

Otherwise get a cardboard archive box to keep it in and just enjoy it! In another 150 years whateer great grandcild gets it will have something of value.