I've just seen your correspondence from a time ago - hope the following is still of some interest.
Without doubt, the family bible belonged to Lt Gen Richard Egerton and his wife Arabella (nee Tomkinson). They were both from Cheshire, and married in 1814. You will find them on the following page which you can take as authoritative:http://www.cracroftspeerage.co.uk/online/content/EgertonB1617.htm
Richard was the youngest son of Philip Egerton of Oulton in Cheshire, and would almost certainly have been born at Oulton Hall. His two oldest brothers succeeded in turn to the Egerton Baronetcy after a senior line of the family died out. Richard himself joined the Army, and was engaged at the Battle of Waterloo - I have in my possession a letter written by him to Arabella in the evening after the battle. He continued to serve with distinction in the Army, but I do not know any details about his subsequent career - for some reason he has rather dropped out of the Egerton family consciousness, and even does not appear in the current version of Burkes.
Arabella's family lived at Dorfold Hall near Nantwich in Cheshire: seehttp://www.thornber.net/cheshire/htmlfiles/tomkinson.html
Richard and Arabella seem to have lived at Eaton Banks (now Arderne Hall) which is very close to Oulton: seehttp://www.parksandgardens.ac.uk/component/option,com_parksandgardens/task,site/id,6807/tab,history/Itemid,292/
Richard seems to have died in 1854, and Arabella in 1860. As far as I know, they had no children. I have a letter written from the Crimea by my great-great grandfather, Caledon Richard Egerton (Richard's nephew) expressing surprise at the size of legacy he had just received out of Richard's Will.
I know of no relationship between the Egerton and Giddings families that would account for your having it. The likely thing is that it would have passed to a relation of Arabella's on her death in 1860, and hence somehow to you. So I think you need to look for a relationship between your ancestors and the Tomkinson family of Dorfold.
I'm sure you are looking after the bible with great love and care - it's a precious object, but I'm sure will be all the more precious to you if you can learn more about the generations that have held it before you. Good luck in your searches.