© 2015 The Authors. We measure the bulk flow of the local Universe using the 6dF Galaxy Survey peculiar velocity sample (6dFGSv), the largest and most homogeneous peculiar velocity sample to date. 6dFGSv is a Fundamental Plane sample of ~104 peculiar velocities covering the whole Southern hemisphere for galactic latitude |b| > 10°, out to redshift z = 0.0537.We apply the 'minimum variance' bulk flow weighting method, which allows us to make a robust measurement of the bulk flow on scales of 50 and 70 h-1 Mpc. We investigate and correct for potential bias due to the lognormal velocity uncertainties, and verify our method by constructing ? cold dark matter (?CDM) 6dFGSv mock catalogues incorporating the survey selection function. For a hemisphere of radius 50 h-1 Mpc we find a bulk flow amplitude of U = 248 ± 58 km s-1 in the direction (l, b) = (318° ± 20°, 40° ± 13°), and for 70 h-1 Mpc we find U = 243 ± 58 km s-1, in the same direction. Our measurement gives us a constraint on s8 of 1.01+1.07 -0.58. Our results are in agreement with other recent measurements of the direction of the bulk flow, and our measured amplitude is consistent with a ?CDM prediction.