We study the shape and kinematics of simulated dwarf galaxy discs in the APOSTLE suite of Lambda cold dark matter (Lambda CDM) cosmological hydrodynamical simulations. We find that a large fraction of these gas-rich, star-forming discs show weak bars in their stellar component, despite being dark-matter-dominated systems. The bar pattern shape and orientation reflect the ellipticity of the dark matter potential, and its rotation is locked to the slow figure rotation of the triaxial dark halo. The bar-like nature of the potential induces non-circular motions in the gas component, including strong bisymmetric flows that can be readily seen as m = 3 harmonic perturbations in the HI line-of-sight velocity fields. Similar bisymmetric flows are seen in many galaxies of The HI Nearby Galaxy Survey (THINGS) and Local Irregulars That Trace Luminosity Extremes THINGS (LITTLE THINGS), although on average their amplitudes are a factor of similar to 2 weaker than in our simulated discs. Our results indicate that bar-like patterns may arise even when baryons are not dominant, and that they are common enough to warrant careful consideration when analysing the gas kinematics of dwarf galaxy discs.