This work explores the feasibility of employing ultrasound (US) US technology in a wrist-worn IoT device for low-power, high-fidelity heart-rate (HR) extraction. US offers deep tissue penetration and can monitor pulsatile arterial blood flow in large vessels and the surrounding tissue, potentially improving robustness and accuracy compared to PPG. We present an IoT wearable system prototype utilizing a commercial microcontroller MCU employing the onboard ADC to capture high frequency US signals and an innovative low-power US pulser. An envelope filter lowers the bandwidth of the US signal by a factor of >5x, reducing the system's acquisition requirements without compromising accuracy (correlation coefficient between HR extracted from enveloped and raw signals, r(92)=0.99, p<0.001). The full signal processing pipeline is ported to fixed point arithmetic for increased energy efficiency and runs entirely onboard. The system has an average power consumption of 5.8mW, competitive with PPG based systems, and the HR extraction algorithm requires only 68kB of RAM and 71ms of processing time on an ARM Cortex-M4 MCU. The system is estimated to run continuously for more than 7 days on a smartwatch battery. To accurately evaluate the proposed circuit and algorithm and identify the anatomical location on the wrist with the highest accuracy for HR extraction, we collected a dataset from 10 healthy adults at three different wrist positions. The dataset comprises roughly 5 hours of HR data with an average of 80.6+-16.3 bpm. During recording, we synchronized the established ECG gold standard with our US-based method. The comparisons yields a Pearson correlation coefficient of r(92)=0.99, p<0.001 and a mean error of 0.69+-1.99 bpm in the lateral wrist position near the radial artery. The dataset and code have been open-sourced at https://github.com/mgiordy/Ultrasound-Heart-Rate