The purpose of this study is to determine whether a medicine called zoledronic acid can reduce fractures in people with Parkinson's disease or parkinsonism. People with Parkinson's disease or parkinsonism have a high risk of fractures related to falls. Zoledronic acid is approved by the U.S. Food and Drug Administration (FDA) for osteoporosis (weak bones); its use in this study is experimental. Participants will be randomly assigned to 1 of 2 study groups. Group 1 will receive a placebo (substance without medicine); Group 2 will receive zoledronic acid via infusion. Study staff will check in with participants every 4 months to ask if they have any falls and any fractures.