We investigate the role of galactic bars in fuelling and triggering Active Galactic Nucleus (AGN) in disc galaxies up to z~0.8. We utilise a Deep Learning model, fine-tuned on Galaxy Zoo volunteer classifications, to identify (strongly and weakly) barred and unbarred disc galaxies in Hyper Suprime-Cam Subaru Strategic Program i-band images. We select AGN using three independent diagnostics: mid-infrared colours, X-ray detections, and spectral energy distribution (SED) fitting. The SED analysis, performed using CIGALE, quantifies the relative AGN contribution to the total galaxy luminosity (f_AGN_) and the AGN luminosity (L_disc_). We assess the impact of bars by comparing AGN incidence and properties in barred galaxies against carefully constructed redshift-, stellar mass-, and colour-matched unbarred control samples. Our binary AGN classification experiment demonstrates that barred disc galaxies host a higher fraction of AGN compared to their unbarred counterparts, though the significance depends on the AGN selection method, with a more modest excess for SED AGN, and control sample size. This suggests a contributing role for bars in the global AGN budget. The contribution of bars to AGN fuelling appears confined to systems where the AGN has a lower relative contribution to the host galaxy's emission (f_AGN_<0.75). Crucially, we find a significant dearth of barred disc galaxies hosting AGN with f_AGN_>0.75, independent of bar strength. Consistent with this, the fraction of barred galaxies among AGN hosts decreases with increasing L_disc_. Combined with previous results, we suggest that bars may contribute to fuelling the population of low-to-moderate luminosity AGN, but major mergers are the principal mechanism for triggering the most powerful and dominant accretion events.