Bone mineral density (BMD) is a clinically critical indicator of osteoporosis, usually measured by dual-energy X-ray absorptiometry (DEXA). Due to the limited accessibility of DEXA machines and examinations, osteoporosis is often under-diagnosed and under-treated, leading to increased fragility fracture risks. Thus it is highly desirable to obtain BMDs with alternative cost-effective and more accessible medical imaging examinations such as X-ray plain films. In this work, we formulate the BMD estimation from plain hip X-ray images as a regression problem. Specifically, we propose a new semi-supervised self-training algorithm to train the BMD regression model using images coupled with DEXA measured BMDs and unlabeled images with pseudo BMDs. Pseudo BMDs are generated and refined iteratively for unlabeled images during self-training. We also present a novel adaptive triplet loss to improve the models regression accuracy. On an in-house dataset of 1,090 images (819 unique patients), our BMD estimation method achieves a high Pearson correlation coefficient of 0.8805 to ground-truth BMDs. It offers good feasibility to use the more accessible and cheaper X-ray imaging for opportunistic osteoporosis screening.