There are tremendous opportunities to advance science, clinical care, sports performance, and societal health if we are able to develop tools for monitoring musculoskeletal loading (e.g., forces on bones or muscles) outside the lab. While wearable sensors enable non-invasive monitoring of human movement in applied situations, current commercial wearables do not estimate tissue-level loading on structures inside the body. Here we explore the feasibility of using wearable sensors to estimate tibial bone force during running. First, we used lab-based data and musculoskeletal modeling to estimate tibial force for ten participants running across a range of speeds and slopes. Next, we converted lab-based data to signals feasibly measured with wearables (inertial measurement units on the foot and shank, and pressure-sensing insoles) and used these data to develop two multi-sensor algorithms for estimating peak tibial force: one physics-based and one machine learning. Additionally, to reflect current running wearables that utilize running impact metrics to infer musculoskeletal loading or injury risk, we estimated tibial force using a commonly measured impact metric, the ground reaction force vertical average loading rate (VALR). Using VALR to estimate peak tibial force resulted in a mean absolute percent error of 9.9%, which was no more accurate than a theoretical step counter that assumed the same peak force for every running stride. Our physics-based algorithm reduced error to 5.2%, and our machine learning algorithm reduced error to 2.6%. Further, to gain insights into how force estimation accuracy relates to overuse injury risk, we computed bone damage expected due to a given loading cycle. We found that modest errors in tibial force translated into large errors in bone damage estimates. For example, a 9.9% error in tibial force using VALR translated into 104% error in estimated bone damage. Encouragingly, the physics-based and machine learning algorithms reduced damage errors to 41% and 18%, respectively. This study highlights the exciting potential to combine wearables, musculoskeletal biomechanics and machine learning to develop more accurate tools for monitoring musculoskeletal loading in applied situations.