Why do bow legged runners get shin splints?

Increased stress. Varus deformity puts more stress on the legs.
Tibial is posterior. Bowl legged people as a result of the tibial inversion have hyperpronated feet. The tibialis posterior tendon and muscle is the one that inverts the foot during gait and when it is over stressed to do so there is abnormal increased pull at the muscles origin off the anterior tibia causing the periosteum it attaches to to become inflamed. This is a shin splint. Custom molded orthotics will stop them.