We report the discovery that Bombus terrestris audax (Buff-tailed bumblebee) locomotor trajectories adhere to a speed-curvature power law relationship which has previously been found in humans, non-human primates and Drosophila larval trajectories. No previous study has reported such a finding in adult insect locomotion. We used behavioural tracking to study walking Bombus terrestris in an arena under different training environments. Trajectories analysed from this tracking show the speed-curvature power law holds robustly at the population level, displaying an exponent close to two-thirds. This exponent corroborates previous findings in human movement patterns, but differs from the three-quarter exponent reported for Drosophila larval locomotion. There are conflicting hypotheses for the principal origin of these speed-curvature laws, ranging from the role of central planning to kinematic and muscular skeletal constraints. Our findings substantiate the latter idea that dynamic power-law effects are robust, differing only through kinematic constraints due to locomotive method. Our research supports the notion that these laws are present in a greater range of species than previously thought, even in the bumblebee. Such power laws may provide optimal behavioural templates for organisms, delivering a potential analytical tool to study deviations from this template. Our results suggest that curvature and angular speed are constrained geometrically, and independently of the muscles and nerves of the performing body.