Using finite element micromagnetic simulations, we study how resonant magnetisation dynamics in thin magnetic discs with perpendicular anisotropy are influenced by magnetostatic coupling to a magnetic nanoparticle. We identify resonant modes within the disc using direct magnetic eigenmode calculations and study how their frequencies and spatial profiles are changed by the nanoparticle's stray magnetic field. We demonstrate that particles can generate shifts in the resonant frequency of the disc's fundamental mode which exceed resonance linewidths in recently studied spin torque oscillator devices. Importantly, it is shown that the simulated shifts can be maintained over large field ranges (here up to 1 T). This is because the resonant dynamics (the basis of nanoparticle detection here) respond directly to the nanoparticle stray field, i.e. detection does not rely on nanoparticle-induced changes to the magnetic ground state of the disc. A consequence of this is that in the case of small disc-particle separations, sensitivities to the particle are highly mode- and particle-position-dependent, with frequency shifts being maximised when the intense stray field localised directly beneath the particle can act on a large proportion of the disc's spins that are undergoing high amplitude precession.