Just to let you know (and I'm taking this from memory), the Bishop Francis Asbury said on his deathbed something to the effect that if anyone named their child after him they would gain great rewards. Of course the Bishop was talking about Heavenly rewards, but a huge amount of people named their sons Francis Asbury Whatever, or gave them a middle name of Asbury. I would say your gg grandfather was probably born within a couple of decades after the Bishop's death in 1816. (This makes it pretty tough to research the surname Asbury as so many people were given the middle name of Asbury that are of no relation at all)

If he was born after 1870, I would say there is a chance he was named after an Asbury relative, as it appears as if people quit naming their children after the Bishop by then.

Craig Asbury

(Asbury and Asberry are the same surname - I won't get into the variation of spelling).