Sensing of a few unpaired electron spins, such as in metal ions and radicals, is a useful but difficult task in nanoscale physics, biology, and chemistry. Single negatively charged nitrogen-vacancy (NV-) centers in diamond offer high sensitivity and spatial resolution in the optical detection of weak magnetic fields produced by a spin bath but often require long acquisition times on the order of seconds. Here, we present an approach based on coupled spin and charge dynamics in dense NV ensembles in strongly fluorescent nanodiamonds (NDs) to sense external magnetic dipoles. We apply this approach to various paramagnetic species, including gadolinium complexes, magnetite nanoparticles, and hemoglobin in whole blood. Taking advantage of the high NV density, we demonstrate a dramatic reduction in acquisition time (down to tens of milliseconds) while maintaining high sensitivity to paramagnetic centers. Strong luminescence, high sensitivity, and short acquisition time make dense NV- ensembles in NDs a potentially promising tool for biosensing and bioimaging applications.