Bishop is a fairly common name, so I imagine that you will find a number of James Bishops in South Carolina.
My suggestion is that you start with your great grandfather Bishop and find him in census reports when he was a child. Ancestry, Family Search and Heritage Quest will all give you access to that. With that you will have the entire family, his parents and siblings. Then start tracking down the siblings in later census reports, always noting all the names, place and dates of birth in their families, in order to know when you find the exact same family in the next more recent census.
It means taking a lot of notes and keeping it organized. When you get to the 20th century, start googling their names and locations. You might be surprised what pops up, including obituaries that list surviving children. This is particularly useful for the past several decades, as it might tell you who could still be alive.
Don't take what you see in various family trees on Ancestry as gospel. There are a lot of assumptions entered as fact by various people, but those assumptions are often either doubtful or flat-out wrong, and they are blindly copied by others into their own family tree. Kinda like a spreading cancer. Always try to verify your findings.
Good hunting! It will be both fun and frustrating, but also satisfying.
A final warning: Beware after you score some good information, lest you become completely obsessed. You will know that you have fallen into that condition when you miss dinner, simply because you're on the hot trail of some good information!