Initial results are presented from 3D MHD modelling of stellar-wind bubbles around O stars moving supersonically through the ISM. We describe algorithm updates that enable high-resolution 3D MHD simulations at reasonable computational cost. We apply the methods to the simulation of the astrosphere of a rotating massive star moving with 30km s−1 through the diffuse interstellar medium, for two different stellar magnetic field strengths, 10G and 100G. Features in the flow are described and compared with similar models for the Heliosphere. The shocked interstellar medium becomes asymmetric with the inclusion of a magnetic field misaligned with the star's direction of motion, with observable consequences. When the Alfv´enic Mach number of the wind is ≤ 10 then the stellar magnetic field begins to affect the structure of the wind bubble and features related to the magnetic axis of the star become visible at parsec scales. Prospects for predicting and measuring non-thermal radiation are discussed.