Recent high-resolution interferometric images of submillimetre galaxies (SMGs) reveal fascinatingly complex morphologies. This raises a number of questions: how does the relative orientation of a galaxy affect its observed submillimetre emission, and does this result in an 'orientation bias' in the selection and analysis of such galaxies in flux-limited cosmological surveys? We investigated these questions using the simba cosmological simulation paired with the dust radiative transfer code powderday. We selected eight simulated SMGs (S-850 greater than or similar to 2 mJy) at z = 2, and measured the variance of their 'observed' emission over 50 random orientations. Each galaxy exhibits significant scatter in its emission close to the peak of the thermal dust emission, with variation in flux density of up to a factor of 2.7. This results in an appreciable dispersion in the inferred dust temperatures and infrared luminosities (16(th)-84(th) percentile ranges of 5 K and 0.1 dex, respectively) and therefore a fundamental uncertainty in derived parameters such as dust mass and star formation rate (similar to 30 per cent for the latter using simple calibrations). Using a Monte Carlo simulation we also assessed the impact of orientation on flux-limited surveys, finding a bias in the selection of SMGs towards those with face-on orientations, as well as those at lower redshifts. We predict that the orientation bias will affect flux-limited single-dish surveys, most significantly at THz frequencies, and this bias should be taken into account when placing the results of targeted follow-up studies in a statistical context.