A study from Manchester Metropolitan University in the UK shows that sprint cyclists have denser bones than long distance cyclists who have denser bones than sedentary control subjects ( Medicine & Science in Sports & Exercise, March 2009). While cyclists have less dense bones than weight lifters and football players, they still have denser bones than people who do not exercise. The greater the force on bones during exercise, the denser the bone. So any type of exercise is good for your bones and a sedentary lifestyle is bad for bones.
When I reported on this study, several readers responded by quoting other studies that showed competitive cyclists have lower bone mineral density in their spines than moderately-active, aged-matched men ( Medicine & Science in Sports & Exercise, February 2009; Osteoporosis International Reports, August 2003). These studies have been interpreted to mean that cycling increases risk for bone fractures beyond what you would expect from just falling off the bike.
I cannot find any studies showing that cycling weakens bones to increase fracture risk. Bone density is associated with bone strength, but does not measure it. The only way to measure bone strength is to see how much force it takes at break a bone. For example, birds have strong bones that are not very dense.
The theory that the act of cycling weakens bones flies in the face of our current understanding of bone metabolism. If indeed cyclists suffer from weak bones (and I do not believe that they do), the cause would be something other than riding a bicycle. Bones are constantly remodeling. Cells called osteoblasts bring in calcium to bones while cells called osteoclasts take calcium out. Any force on bones increases, and lack of force decreases, the rate of bone formation. Astronauts in space lose bone because lack of force blocks their ability to respond to Insulin Like Growth Factor-1 that stimulates bone growth ( Journal of Bone and Mineral Research, March 2004). All competitive cyclists know that hammering on the pedals while pulling up on their handle bars puts tremendous force on every muscle and bone in their bodies, and this should stimulate bone growth.