Bayesian methods promise enhanced device performance and accelerated data collection. We demonstrate an adaptive Bayesian measurement strategy for atom number estimation in a quantum technology experiment, utilising a symmetry-informed loss function. Compared to a standard unoptimised strategy, our method yields a five-fold reduction in the fractional variance of the atom number estimate. Equivalently, it achieves the target precision with 40% fewer data points. We provide general expressions for the optimal estimator and error for any quantity amenable to symmetry-informed strategies, facilitating the application of these strategies in quantum computing, communication, metrology, and the wider quantum technology sector.