I don't think this bible is connected to your Bullock family line. I found your tree and other trees that trace the Richard Henry Bullock line further back than you have. There is nothing in common with the William Bullock of the bible.
Your line is in Georgia, North Carolina and Virginia then back to England. William's line is New York and Massachusetts then England, with no common people among the two lines, at least back to the 1500's.
The Polly I mentioned married into the Bullock line. She was born Polly Phillips, to Jonathon and Jemima (Palmer) Phillips. So this is not the same Polly Bullock as in your tree.