Despite the evidence that supermassive black holes (SMBHs) co-evolve with their host galaxy, and that most of the growth of these SMBHs occurs via merger-free processes, the underlying mechanisms which drive this secular co-evolution are poorly understood. We investigate the role that both strong and weak large-scale galactic bars play in mediating this relationship. Using 72,940 disc galaxies in a volume-limited sample from Galaxy Zoo DESI, we analyse the active galactic nucleus (AGN) fraction in strongly barred, weakly barred, and unbarred galaxies up to z = 0.1 over a range of stellar masses and colours. After controlling for stellar mass and colour, we find that the optically selected AGN fraction is 31.6 ± 0.9 per cent in strongly barred galaxies, 23.3 ± 0.8 per cent in weakly barred galaxies, and 14.2 ± 0.6 per cent in unbarred disc galaxies. These are highly statistically robust results, strengthening the tantalising results in earlier works. Strongly barred galaxies have a higher fraction of AGNs than weakly barred galaxies, which in turn have a higher fraction than unbarred galaxies. Thus, while bars are not required in order to grow a SMBH in a disc galaxy, large-scale galactic bars appear to facilitate AGN fuelling, and the presence of a strong bar makes a disc galaxy more than twice as likely to host an AGN than an unbarred galaxy at all galaxy stellar masses and colours.