Globular clusters (GCs) are proxies of the formation assemblies of their host galaxies. However, few studies exist targeting GC systems of spiral galaxies up to several effective radii. Through 12-band Javalambre Photometric Local Universe Survey (J-PLUS) imaging, we study the point sources around the M 81/M 82/NGC 3077 triplet in search of new GC candidates. We develop a tailored classification scheme to search for GC candidates based on their similarity to known GCs via a principal component analysis projection. Our method accounts for missing data and photometric errors. We report 642 new GC candidates in a region of 3.5 deg2 around the triplet, ranked according to their Gaia astrometric proper motions when available. We find tantalizing evidence for an overdensity of GC candidate sources forming a bridge connecting M 81 and M 82. Finally, the spatial distribution of the GC candidates (g - i) colours is consistent with halo/intra-cluster GCs, i.e. it gets bluer as they get further from the closest galaxy in the field. We further employ a regression-tree-based model to estimate the metallicity distribution of the GC candidates based on their J-PLUS bands. The metallicity distribution of the sample candidates is broad and displays a bump towards the metal-rich end. Our list increases the population of GC candidates around the triplet by threefold, stresses the usefulness of multiband surveys in finding these objects, and provides a testbed for further studies analysing their spatial distribution around nearby (spirals) galaxies.