With consistent strength training, 2 or 3 times a week, bones begin the gradual process of getting stronger and the amount varies from individual to individual. In the early 1990s, Tufts University had the first research study to see if post-menopausal women could increase their bone density with strength training. Sedentary, post-menopausal women were recruited and either placed in the strength training group or in the control group, (who unfortunately, for the control group, had to stay sedentary for another year)! The strength training group gained an average of 1% bone mass and the control group lost 2 to 2.5% bone mass.
The lead researcher of this study, Miriam Nelson, PhD, wrote the excellent books Strong Women Stay Young and Strong Women, Strong Bones. The books weren't written in particular for those who already have bone loss, so make sure that you run the exercises by your healthcare provider to make sure that they're appropriate for you. Most of the exercises are done with a neutral spine, but the abdominal exercises are done lifting the upper body, which National Osteoporosis Foundation (NOF) affiliated physical therapists (PT) don’t recommend. The back extension done by pushing back against a machine with one’s back is also questionable. Ask your doc or PT for individual guidance before trying these or any other exercises.
Dr. Nelson wrote Strong Women Stay Young in response to requests for specific information after her 1994 research was published in JAMA about the good effects of resistance training for women in regards to strength and bone density. They have a LOT of excellent information, are very inspiring, and could be a good place to start in educating yourself on how to get going with a sound exercise program. Your library most likely has a copy.