Bone surface reconstruction is an essential component of computer-assisted orthopedic surgery(CAOS), forming the foundation for both preoperative planning and intraoperative guidance. Compared to traditional imaging modalities such as computed tomography (CT) and magnetic resonance imaging (MRI),ultrasound, an emerging CAOS technology, provides a radiation-free, cost-effective, and portable alternative. While ultrasound offers new opportunities in CAOS, technical shortcomings continue to hinder its translation into surgery. In particular, due to the inherent limitations of ultrasound imaging, B-mode ultrasound typically captures only partial bone surfaces. The inter- and intra-operator variability in ultrasound scanning further increases the complexity of the data. Existing reconstruction methods struggle with such challenging data, leading to increased reconstruction errors and artifacts, such as holes and inflated structures. Effective techniques for accurately reconstructing open bone surfaces from real-world 3D ultrasound volumes remain lacking. We propose UltraBoneUDF, a self-supervised framework specifically designed for reconstructing open bone surfaces from ultrasound data. It learns unsigned distance functions (UDFs) from 3D ultrasound data. In addition, we present a novel loss function based on local tangent plane optimization that substantially improves surface reconstruction quality. UltraBoneUDF and competing models are benchmarked on three open-source datasets and further evaluated through ablation studies. Qualitative results demonstrate the limitations of the state-of-the-art methods. Quantitatively, UltraBoneUDF achieves comparable or lower bi-directional Chamfer distance across three datasets with fewer parameters: 1.60 mm on the UltraBones100k dataset (~25.5% improvement), 0.21 mm on the OpenBoneCT dataset, and 0.18 mm on the ClosedBoneCT dataset.