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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, which is much faster than any other reported technique. We achieve this unprecedented speed by tuning the nanomagnetic properties of the films, including the Dzyaloshinskii-Moriya interaction, in the first application of topological protection from the skyrmion state to a nanoparticle sensor. We demonstrate the technique on iron/nickel nanorods and iron oxide nanoparticles, which delineate a wide range of properties and applications. Bubble magnetometry enables the first measurement with high throughput for statistical analysis of the magnetic hysteresis of dispersed nanoparticles, and the first direct measurement of a transition from superparamagnetic behavior as single nanoparticles to collective behavior in nanoscale agglomerates. These results demonstrate a breakthrough capability for measuring the heterogeneity and interaction of magnetic nanoparticles., Comment: 18 pages, 10 figures, major revisions since initial submission