The first method involves culture of bone marrow cells under different conditions, with or without supplements to the growth medium which include ascorbic acid and beta-glycerophosphate. If bone growth is activated, the bone-forming cells will begin to express alkaline phosphatase, which can be detected by adding para-nitrophenol phosphate to the dish containing the cells and measuring the accumulation of the yellow product of the reaction between alkaline phosphatase and para-nitrophenol phosphate. The experiment is easy to do, but requires the experimenter to have access to cell culture facilities and knowledge of laboratory safety techniques.

The second method would be easier to do, requiring only weighing the bones resulting from various treatments, but would require handling and treatment of live animals.

If he really wants to do something involving bones, he could make a model of bone by having one process simulate the laying down of new bone and one process simulate the resorption of bone. For example, he could apply coats of white paint with one brush and paint remover with another, and simulate various diseases such as osteopetrosis or osteoporosis by diluting the mixtures.

If he's more interested in simulating a process that goes on in the body, perhaps he could do the digestive system. That would simply require a container with HCl(Muriatic acid at the hardware store), with an item submerged in it that would slowly get dissolved. You could simulate indigestion by adding more things, and show the effect of antacids.

I wish I could give you a better answer, but as far as I know, to do something actually involving real bone growth he'd have to use a live animal of some sort.