We propose an interpretation for the signal asymmetry observed in anomalous Hall effect (AHE) transport measurements of magnetic nanostructures patterned from bilayer magnetic thin films. Experimental data and simulations demonstrate that the signal asymmetry observed in hysteresis loops arises due to a combination of the anomalous Hall effect together with a contribution from longitudinal giant magnetoresistance (GMR). The effect shows a high-sensitivity to nanoscale misalignments in Hall cross geometry. Consequently, the complex nature of the origin of electrical signals should be taken into account when undertaking any transport measurements on magnetic bilayer nanostructures, such as GMR or spintronic devices.