We present hydrodynamic simulations of stellar wind-magnetosphere interactions in hot Jupiters such as WASP-12b. For fiducial stellar wind rates we find that a planetary magnetic field of a few G produces a large magnetospheric cavity, which is typically 6-9 planetary radii in size. A bow shock invariably forms ahead of the magnetosphere, but the pre-shock gas is only mildly supersonic (with typical Mach numbers of ≃ 1.6-1.8) so the shock is weak. This results in a characteristic signature in the ultraviolet light curve: a broad absorption feature that leads the optical transit by 10-20% in orbital phase. The shapes of our synthetic lightcurves are consistent with existing observations of WASP-12b, but the required near-UV optical depth (τ ∼ 0.1) can only be achieved if the shocked gas cools rapidly. We further show that radiative cooling is inefficient, so we deem it unlikely that a magnetospheric bow shock is responsible for the observed near-UV absorption. Finally, we apply our model to two other well-studied hot Jupiters (WASP-18b and HD209458b), and suggest that UV observations of more massive short-period planets (such as WASP-18b) will provide a straightforward test to distinguish between different models of circumplanetary absorption.