Bubbles have a rich history as transducers in particle-physics experiments. In a solid-state analogue, we use bubble domains in nanomagnetic films to measure magnetic nanoparticles. This technique can determine the magnetic orientation of a single nanoparticle in a fraction of a second and generate a full hysteresis loop in a few seconds. We achieve this high throughput by tuning the nanomagnetic properties of the films, including the Dzyaloshinskii-Moriya interaction, in an application of topological protection from the skyrmion state to a nanoparticle sensor. We develop the technique on nickel-iron nanorods and iron-oxide nanoparticles, which delineate a wide range of properties and applications. Bubble magnetometry enables precise statistical analysis of the magnetic hysteresis of dispersed nanoparticles, and direct measurement of a transition from superparamagnetic behavior as single nanoparticles to collective behavior in nanoscale agglomerates. These results demonstrate a practical capability for measuring the heterogeneity and interaction of magnetic nanoparticles.