Strong bursts of star formation in galaxies may be triggered either by internal or external mechanisms. We study the distribution and kinematics of the H I gas in the outer regions of 18 nearby starburst dwarf galaxies that have accurate star formation histories from Hubble Space Telescope observations of resolved stellar populations. We find that starburst dwarfs show a variety of H I morphologies, ranging from heavily disturbed H I distributions with major asymmetries, long filaments, and/or H I-stellar offsets to lopsided H I distributions with minor asymmetries. We quantify the outer H I asymmetry for both our sample and a control sample of typical dwarf irregulars. Starburst dwarfs have more asymmetric outer H I morphologies than typical irregulars, suggesting that some external mechanism triggered the starburst. Moreover, galaxies hosting an old burst (≳100 Myr) have more symmetric H I morphologies than galaxies hosting a young one (≲100 Myr), indicating that the former ones probably had enough time to regularize their outer H I distribution since the onset of the burst. We also investigate the nearby environment of these starburst dwarfs and find that most of them (˜80 per cent) have at least one potential perturber at a projected distance ≲200 kpc. Our results suggest that the starburst is triggered either by past interactions/mergers between gas-rich dwarfs or by direct gas infall from the intergalactic medium.