Pocket-sized, low-cost point-of-care ultrasound (POCUS) devices are increasingly used in musculoskeletal (MSK) applications for structural examination of bone tissue. However, the image quality in MSK ultrasound is often limited by speckle noise, low resolution, poor contrast, and anisotropic reflections, making bone images difficult to interpret without additional post-processing. Typically, medical ultrasound systems use delay and sum beamforming (DASB) for image reconstruction, which is not specifically optimized for bone structures. To address these limitations, we propose BEAM-Net, a novel end-to-end deep neural network (DNN) that performs high-frame-rate ultrasound beamforming with integrated bone enhancement, using single-plane-wave (SPW) radio frequency (RF) data as input. Our approach embeds a Bone Probability Map (BPM), which acts as an attention mechanism to enforce higher structural similarity around bony regions in the image. The proposed approach is the first of its kind to incorporate bone enhancement directly into ultrasound beamforming using deep learning. BEAM-Net was trained and evaluated on in-vivo MSK and synthetic RF ultrasound datasets. This paper introduces the Edge Preservation Index (EPI) as a new region-focused metric for evaluating structural fidelity in bone-enhanced ultrasound images. The performance of BEAM-Net was compared with conventional DASB and existing deep learning architectures using the EPI, Contrast Ratio (CR), Signal-to-Noise ratio (SNR), Speckle Similarity Index (SSI), and Structural Similarity Index (SSIM). BEAM-Net showed substantial gains over SPW-DASB, achieving 51.4-51% higher CR and 94.2-73.3% higher SNR on in-vivo MSK and synthetic RF datasets. It outperformed multiple steered plane wave DASB (MPW-DASB), with 19.8-24.0% improvements in CR and SNR on in-vivo MSK and 2.5-12.8% improvements on synthetic data.