I am not aware of any reports showing that tanning beds improve BMD. However, there are few articles showing that the levels of vitamin D is higher in tanning bed users.
UV and dietary predictors of serum 25-hydroxyvitamin D concentrations among young shift-working nurses and implications for bone density and skin cancer.
Public Health Nutr 04/01/2014 0
Vitamin D status relative to diet, lifestyle, injury, and illness in college athletes.
Med Sci Sports Exerc 02/01/2011 1
Tanning is associated with optimal vitamin D status (serum 25-hydroxyvitamin D concentration) and higher bone mineral density.
Am J Clin Nutr 12/01/2004