Rb2Cu2Mo3O12 is a quasi-one-dimensional frustrated S=1/2 multiferroic that displays magnetic field-tunable ferroelectricity with no long-range magnetic order. To interrogate this intriguing behavior we employed dielectric measurements, neutron diffraction, and muon spin spectroscopy to study powder samples at mK temperatures and tesla magnetic fields. Subtle signatures in the experimental data allow the identification of different dielectric and magnetic regimes, none of which conclusively suggest the existence of magnetic long-range order. The results are broadly consistent with the system hosting a gapped nonmagnetic ground state in zero field, that undergoes a magnetic field-induced transition at ∼2 T into a phase with a static, disordered spin arrangement. We discuss our results in the context of previous work on this system, and conclude that the origin of a magnetic field-dependent electric polarization with no long-range magnetic order could call for a new paradigm of magnetically driven ferroelectricity.