Contrary to common belief, bilayer graphene is not defect-free: the abundance of partial dislocations leads to a mosaic-like network structure. As a result, as now shown, the magnetoresistance of bilayer graphene depends linearly, rather than quadratically, on the external magnetic field. The magnetoresistance of conductors usually has a quadratic dependence on magnetic field1, however, examples exist of non-saturating linear behaviour in diverse materials2,3,4,5,6. Assigning a specific microscopic mechanism to this unusual phenomenon is obscured by the co-occurrence and interplay of doping, mobility fluctuations and a polycrystalline structure7,8. Bilayer graphene has virtually no doping fluctuations, yet provides a built-in mosaic tiling due to the dense network of partial dislocations9,10. We present magnetotransport measurements of epitaxial bilayer graphene that exhibits a strong and reproducible linear magnetoresistance that persists to B = 62 T at and above room temperature, decorated by quantum interference effects at low temperatures. Partial dislocations thus have a profound impact on the transport properties in bilayer graphene, a system that is frequently assumed to be dislocation-free. It further provides a clear and tractable model system for studying the unusual properties of mosaic conductors.