Liftmor is a clinical trial from the The Bone Clinic in Australia that had postmenopausal women (some with a history of fractures) lifting very heavy weights (barbells for deadlift) and two other High Intensity strength training exercises for 30 minutes twice a week. At the end of 8 months there was a gain of BMD. The women were supervised by physiotherapists - not personal trainers as they felt they needed the expertise to make sure these women had perfect form first before attempting the deadlifts and that they continued having perfect form. Just google Bone Clinic of Australia or Liftmor for further details. They now have a program called Onero- it is a franchise but I think there are only two of them so far in the US- Pennsylvania and New Jersey.
There are others in this forum or the Inspire forum who have reported on using personal trainers for the same exercises or personal trainers for using machines at the gym, with success in increasing BMD.
The BEST clinical trial used the machines at a gym.