J,
I've never done a project like that, so please take my advice with a grain of salt. I have seen something like that, though, in a book, and it appears that that the author used two pieces of leather to accomplish it. One piece was cut to fit the base exactly, and the second piece was wrapped around the cylinder and then stitched (or laced) to the base.
I tend to cut corners quite a bit and stay away from complex constructions. Unless there's a reason why you want the base of the bucket to be covered, why don't you simply wrap a properly-sized piece of leather around the cylinder part and then lace or stitch up the seam?
Good luck, -Alex