We study the influence of the presence of a strong bar in disc galaxies which host an active galactic nucleus (AGN). Using data from the Sloan Digital Sky Survey and morphological classifications from the Galaxy Zoo 2 project, we create a volume-limited sample of 19 756 disc galaxies at 0.01 < z < 0.05 which have been visually examined for the presence of a bar. Within this sample, AGN host galaxies have a higher overall percentage of bars (51.8 per cent) than inactive galaxies exhibiting central star formation (37.1 per cent). This difference is primarily due to known effects: that the presence of both AGN and galactic bars is strongly correlated with both the stellar mass and integrated colour of the host galaxy. We control for this effect by examining the difference in AGN fraction between barred and unbarred galaxies in fixed bins of mass and colour. Once this effect is accounted for, there remains a small but statistically significant increase that represents 16 per cent of the average barred AGN fraction. Using the L[Oiii]/MBH ratio as a measure of AGN strength, we show that barred AGNs do not exhibit stronger accretion than unbarred AGNs at a fixed mass and colour. The data are consistent with a model in which bar-driven fuelling does contribute to the probability of an actively growing black hole, but in which other dynamical mechanisms must contribute to the direct AGN fuelling via smaller, non-axisymmetric perturbations.