According to the British Geological Survey map for the area, the Boneywell lies on a thin slither of Silurian Aymestry Limestone, which it describes as "generally comprising carbonate material (coral, shell fragments), forming beds and locally reefs." This might explain the boneyness of the well, though the surrounding rocks in the area aren't vastly different. An alternative explanation was given by the 1800s geologist, Roderich Murchison, who apparently tested bones in the well and found them to be almost entirely frog bones. He suggested that animals dying above the spring, and in the surrounding cracks, were filtered through the fissures around the spring so only small bones were left. These speculations, and a great deal of other information about the spring, including photos and drawings, can be found in:
Shaw, T.E. (1994) The Bonewell Spring (England) in Valvasor's "Die Ehre Dess Herzogthums Crain" (1689) - the Author's Sources Acta Carsologica XXIII, 359-367.
Which can be downloaded by clicking the title. Shaw notes that the spring is capped and water being extracted from it, which explains why the current stream is much less than sketches of the spring show from the 1700s (see Myth).